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Deck 2: Systems of Linear Equations and Matrices

ملء الشاشة (f)
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سؤال
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution <div style=padding-top: 35px> ​

A) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution <div style=padding-top: 35px>
B) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution <div style=padding-top: 35px>
C) infinitely many solutions <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution <div style=padding-top: 35px>
D) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution <div style=padding-top: 35px>
E) no solution
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سؤال
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px> ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
D) No solution
سؤال
Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.

A) <strong>Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.</strong> A) B) C) D) <div style=padding-top: 35px>
B) <strong>Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.</strong> A) B) C) D) <div style=padding-top: 35px>
C) <strong>Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.</strong> A) B) C) D) <div style=padding-top: 35px>
D) <strong>Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.</strong> A) B) C) D) <div style=padding-top: 35px>
سؤال
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px> ​

A) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
B) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
C) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
D) infinitely many solutions <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
E) no solution
سؤال
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px> ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
D) No solution
سؤال
Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of nitrogen, <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of phosphate, and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of potassium. A 100-lb bag of grade-B fertilizer contains <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of nitrogen and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of nitrogen, <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of phosphate, and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of nitrogen, <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of phosphate, and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> lb of potassium are available and all the nutrients are used?

A) <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> , <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> 100-lb bags correspondingly
B) <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> , <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> 100-lb bags correspondingly
C) <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> , <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> 100-lb bags correspondingly
D) <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> , <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution <div style=padding-top: 35px> 100-lb bags correspondingly
E) the problem has no solution
سؤال
Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.

A) <strong>Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.</strong> A) B) C) D) <div style=padding-top: 35px>
B) <strong>Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.</strong> A) B) C) D) <div style=padding-top: 35px>
C) <strong>Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.</strong> A) B) C) D) <div style=padding-top: 35px>
D) <strong>Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.</strong> A) B) C) D) <div style=padding-top: 35px>
سؤال
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) <div style=padding-top: 35px> ​

A) One and only one solution;( <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) <div style=padding-top: 35px> , <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) <div style=padding-top: 35px> )
B) No solution
C) One and only one solution; ( <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) <div style=padding-top: 35px> , <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) <div style=padding-top: 35px> )
D) Infinitely many solutions
E) One and only one solution; ( <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) <div style=padding-top: 35px> , <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) <div style=padding-top: 35px> )
سؤال
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px> ​

A) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
B) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
C) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
D) infinitely many solutions <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
E) no solution
سؤال
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px> ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
D) No solution
سؤال
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px> ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
D) No solution
سؤال
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px> ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
D) No solution
سؤال
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px> ​

A) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
B) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
C) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
D) infinitely many solutions <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution <div style=padding-top: 35px>
E) no solution
سؤال
Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.

A) <strong>Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.</strong> A) B) C) D) <div style=padding-top: 35px>
B) <strong>Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.</strong> A) B) C) D) <div style=padding-top: 35px>
C) <strong>Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.</strong> A) B) C) D) <div style=padding-top: 35px>
D) <strong>Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.</strong> A) B) C) D) <div style=padding-top: 35px>
سؤال
Determine the value of k for which the system of linear equations has no solution. ​ <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px> ​

A) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
Formulate but do not solve the problem. ​
The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn.
​

A) <strong>Formulate but do not solve the problem. ​ The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn. ​</strong> A) ​ B) ​ C) ​ D) ​ <div style=padding-top: 35px> ​
B) <strong>Formulate but do not solve the problem. ​ The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn. ​</strong> A) ​ B) ​ C) ​ D) ​ <div style=padding-top: 35px> ​
C) <strong>Formulate but do not solve the problem. ​ The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn. ​</strong> A) ​ B) ​ C) ​ D) ​ <div style=padding-top: 35px> ​
D) <strong>Formulate but do not solve the problem. ​ The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn. ​</strong> A) ​ B) ​ C) ​ D) ​ <div style=padding-top: 35px> ​
سؤال
Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are <div style=padding-top: 35px> ​

A) <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are <div style=padding-top: 35px> . The solutions are <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are <div style=padding-top: 35px>
B) <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are <div style=padding-top: 35px> . The solutions are <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are <div style=padding-top: 35px>
C) <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are <div style=padding-top: 35px> . The solutions are <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are <div style=padding-top: 35px>
D) <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are <div style=padding-top: 35px> . The solutions are <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are <div style=padding-top: 35px>
سؤال
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px> ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
D) No solution
سؤال
Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E) <div style=padding-top: 35px> units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E) <div style=padding-top: 35px> times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.

A) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.

A) <strong>Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.</strong> A) B) C) D) <div style=padding-top: 35px>
B) <strong>Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.</strong> A) B) C) D) <div style=padding-top: 35px>
C) <strong>Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.</strong> A) B) C) D) <div style=padding-top: 35px>
D) <strong>Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.</strong> A) B) C) D) <div style=padding-top: 35px>
سؤال
Solve the linear system of equations. If the system is inconsistent, indicate this.
​ Solve the linear system of equations. If the system is inconsistent, indicate this. ​ <div style=padding-top: 35px>
سؤال
Formulate but do not solve the problem.
​
The Johnson Farm has 600 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $46 and $23/acre, respectively. Jacob Johnson has $18,400 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant?
سؤال
Formulate but do not solve the problem. ​
A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks.
​

A) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. <div style=padding-top: 35px>
سؤال
Solve the linear system of equations. If the system is inconsistent, indicate this. Solve the linear system of equations. If the system is inconsistent, indicate this. <div style=padding-top: 35px>
سؤال
Solve the linear system of equations. If the system is inconsistent, indicate this. Solve the linear system of equations. If the system is inconsistent, indicate this. <div style=padding-top: 35px>
سؤال
Solve the linear system of equations. If the system is inconsistent, indicate this.
​ Solve the linear system of equations. If the system is inconsistent, indicate this. ​ <div style=padding-top: 35px>
سؤال
Solve the linear system of equations. If the system is inconsistent, indicate this. Solve the linear system of equations. If the system is inconsistent, indicate this. <div style=padding-top: 35px>
سؤال
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. <div style=padding-top: 35px>
سؤال
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.
​ Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <div style=padding-top: 35px>
سؤال
Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.

A) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
Determine the value of k for which the system of linear equations has no solution.
​ Determine the value of k for which the system of linear equations has no solution. ​ ​ k = __________<div style=padding-top: 35px> ​
k = __________
سؤال
Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show?
Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.

A) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
Solve the linear system of equations. If the system is inconsistent, indicate this.
​ Solve the linear system of equations. If the system is inconsistent, indicate this. ​ <div style=padding-top: 35px>
سؤال
Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.

A) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. <div style=padding-top: 35px>
سؤال
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px> ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution <div style=padding-top: 35px>
D) No solution
سؤال
Solve the linear system of equations. If the system is inconsistent, indicate this. Solve the linear system of equations. If the system is inconsistent, indicate this. <div style=padding-top: 35px>
سؤال
A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are parallel.

A) true
B) false
سؤال
Formulate but do not solve the problem.
​
Michael Perez has a total of $1,500 on deposit with two savings institutions. One pays interest at the rate of 8%/year, whereas the other pays interest at the rate of 5%/year. If Michael earned a total of $96 in interest during a single year, how much does he have on deposit in each institution?
سؤال
Formulate but do not solve the problem.
​
The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $1.50/lb. If the blended coffee sells for $2.10/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.)
سؤال
A dietitian wishes to plan a meal around three foods. The percentage of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods is summarized in the accompanying table. A dietitian wishes to plan a meal around three foods. The percentage of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods is summarized in the accompanying table. Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100% of each). __________ ounces of Food I __________ ounces of Food II __________ ounces of Food III<div style=padding-top: 35px> Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100% of each).
__________ ounces of Food I
__________ ounces of Food II
__________ ounces of Food III
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) ( 23, 7 ) B) ( 33, 7 ) C) ( 28, -12 ) D) ( -7, 28 ) E) ( 28, -7 ) <div style=padding-top: 35px>

A) ( 23, 7 )
B) ( 33, 7 )
C) ( 28, -12 )
D) ( -7, 28 )
E) ( 28, -7 )
سؤال
Determine whether the statement is true or false.
​
A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are nonparallel.
سؤال
Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of nitrogen, Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of phosphate, and Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of potassium. A 100-lb bag of grade-B fertilizer contains Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of nitrogen and Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of nitrogen, Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of phosphate, and Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of nitrogen, Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of phosphate, and Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags<div style=padding-top: 35px> lb of potassium are available and all the nutrients are used?
​
grade-A fertilizer: __________ 100-lb bags
​
grade-B fertilizer: __________ 100-lb bags
​
grade-C fertilizer: __________ 100-lb bags
سؤال
Formulate but do not solve the problem.
​
The total number of passengers riding a certain city bus during the morning shift is 1,000. If the child's fare is $0.65, the adult fare is $0.35, and the total revenue from the fares in the morning shift is $440, how many children and how many adults rode the bus during the morning shift?
سؤال
Formulate but do not solve the problem.
​
Kelly Fisher has a total of $32,000 invested in two municipal bonds that have yields of $5% and $6% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,740, how much does she have invested in each bond?
سؤال
Pivot the system about the bolded element. ​ <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px> ​

A) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination <strong>Solve the system of linear equations using the Gauss-Jordan elimination </strong> A) ( 5, -18, -12 ) B) ( -21, 5, 12 ) C) ( 12, -18, -5 ) D) ( 18, 5, 12 ) E) ( 18, -5, -12 ) <div style=padding-top: 35px>

A) ( 5, -18, -12 )
B) ( -21, 5, 12 )
C) ( 12, -18, -5 )
D) ( 18, 5, 12 )
E) ( 18, -5, -12 )
سؤال
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is not in row-reduced form. B) The matrix is in row-reduced form. <div style=padding-top: 35px>

A) The matrix is not in row-reduced form.
B) The matrix is in row-reduced form.
سؤال
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is in row-reduced form. B) The matrix is not in row-reduced form. <div style=padding-top: 35px>

A) The matrix is in row-reduced form.
B) The matrix is not in row-reduced form.
سؤال
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is not in row-reduced form. B) The matrix is in row-reduced form. <div style=padding-top: 35px>

A) The matrix is not in row-reduced form.
B) The matrix is in row-reduced form.
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) ( 5, -2, -3 ) B) ( 3, -2, -5 ) C) ( -5, 3, 5 ) D) ( 2, -3, 5 ) E) ( 2, 3, 5 ) <div style=padding-top: 35px>

A) ( 5, -2, -3 )
B) ( 3, -2, -5 )
C) ( -5, 3, 5 )
D) ( 2, -3, 5 )
E) ( 2, 3, 5 )
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) ( 8, -3 ) B) ( 7, -2 ) C) ( 2, -7 ) D) ( -7, 2 ) E) ( -8, -2 ) <div style=padding-top: 35px>

A) ( 8, -3 )
B) ( 7, -2 )
C) ( 2, -7 )
D) ( -7, 2 )
E) ( -8, -2 )
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) ( 2, -10, -12 ) B) ( 12, -10, -2 ) C) ( -15, 12, 2 ) D) ( 10, 12, -2 ) E) ( 10, 12, 2 ) <div style=padding-top: 35px>

A) ( 2, -10, -12 )
B) ( 12, -10, -2 )
C) ( -15, 12, 2 )
D) ( 10, 12, -2 )
E) ( 10, 12, 2 )
سؤال
Write the augmented matrix corresponding to the given system of equations. <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E) <div style=padding-top: 35px> <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E) <div style=padding-top: 35px>

A) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is not in row-reduced form. B) The matrix is in row-reduced form. <div style=padding-top: 35px>

A) The matrix is not in row-reduced form.
B) The matrix is in row-reduced form.
سؤال
Solve the system of linear equations, using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px>

A) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px> , y = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px> , z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px>
B) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px> , y = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px> , z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px>
C) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px> , y = 0, z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px>
D) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px> , y = 0, z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px>
E) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px> , y = 0, z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = <div style=padding-top: 35px>
سؤال
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is in row-reduced form. B) The matrix is not in row-reduced form. <div style=padding-top: 35px>

A) The matrix is in row-reduced form.
B) The matrix is not in row-reduced form.
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E) <div style=padding-top: 35px>

A) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
The annual interest on Sid Carrington's three investments amounted to $35,100: 6% on a savings account, 9% on mutual funds, and 12% on bonds. If the amount of Sid's investment in bonds was triple the amount of his investment in the savings account, and the interest earned from his investment in bonds was equal to the dividends he received from his investment in mutual funds, find how much money he placed in each type of investment. ​

A) $180,000 in a savings account, $45,000 in mutual funds, $135,000 in bonds
B) $135,000 in a savings account, $180,000 in mutual funds, $45,000 in bonds
C) $180,000 in a savings account, $135,000 in mutual funds, $45,000 in bonds
D) $45,000 in a savings account, $180,000 in mutual funds, $135,000 in bonds
E) $45,000 in a savings account, $135,000 in mutual funds, $180,000 in bonds
سؤال
Solve the system of linear equations, using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px>

A) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x3 = 0
B) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x3 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px>
C) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x3 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px>
D) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x3 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px>
E) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 <div style=padding-top: 35px> , x3 = 0
سؤال
The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $2.50/lb. If the blended coffee sells for $2.90/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.) ​

A) 20 lb of $3.00/lb coffee and 80 lb of $2.50/lb coffee
B) 75 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee
C) 80 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee
D) 80 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee
E) 85 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee
سؤال
A theater has a seating capacity of 750 and charges $2 for children, $4 for students, and $5 for adults. At a certain screening with full attendance, there were one-fourth as many adults as children and students combined. The receipts totaled $2,150. How many children attended the show?
​
__________ children
سؤال
An executive of Trident Communications recently traveled to London, Paris, and Rome. He paid $170, $230, and $150/night for lodging in London, Paris, and Rome, respectively, and his hotel bills totaled $4,240. He spent $110, $130, and $100/day for his meals in London, Paris, and Rome, respectively, and his expenses for meals totaled $2,670. If he spent as many days in London as he did in Paris and Rome combined, how many days did he stay in each city? ​

A) 14 days in London, 5 days in Paris, 9 days in Rome
B) 12 days in London, 5 days in Paris, 7 days in Rome
C) 16 days in London, 7 days in Paris, 9 days in Rome
D) 7 days in London, 5 days in Paris, 12 days in Rome
E) 14 days in London, 7 days in Paris, 7 days in Rome
سؤال
Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​

A) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $38 and $30/acre, respectively. Jacob Johnson has $16,600 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? ​

A) 250 acres of corn and 300 acres of wheat
B) 300 acres of corn and 200 acres of wheat
C) 450 acres of corn and 50 acres of wheat
D) 200 acres of corn and 300 acres of wheat
E) 200 acres of corn and 350 acres of wheat
سؤال
Write the system of equations corresponding to the given augmented matrix.
​ Write the system of equations corresponding to the given augmented matrix. ​ <div style=padding-top: 35px>
سؤال
Write the augmented matrix corresponding to the given system of equations. Write the augmented matrix corresponding to the given system of equations. <div style=padding-top: 35px>
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method. <div style=padding-top: 35px>
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method. <div style=padding-top: 35px>
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method. <div style=padding-top: 35px>
سؤال
Write the augmented matrix corresponding to the given system of equations. Write the augmented matrix corresponding to the given system of equations. <div style=padding-top: 35px>
سؤال
Solve the system of linear equations, using the Gauss-Jordan elimination method. Solve the system of linear equations, using the Gauss-Jordan elimination method. x = __________ y =__________ z =__________<div style=padding-top: 35px>
x = __________
y =__________
z =__________
سؤال
A dietitian wishes to plan a meal around three foods. The percent of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods is summarized in the table. Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100% of each). <strong>A dietitian wishes to plan a meal around three foods. The percent of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods is summarized in the table. Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100% of each). ​</strong> A) Food I 10 ounces, Food II 5 ounces, Food III 6 ounces ​ B) Food I 4 ounces, Food II 2 ounces, Food III 5 ounces ​ C) Food I 12 ounces, Food II 16 ounces, Food III 10 ounces ​ D) Food I 10 ounces, Food II 16 ounces, Food III 12 ounces ​ E) Food I 6 ounces, Food II 13 ounces, Food III 10 ounces ​ <div style=padding-top: 35px> ​

A) Food I 10 ounces,
Food II 5 ounces,
Food III 6 ounces
​
B) Food I 4 ounces,
Food II 2 ounces,
Food III 5 ounces
​
C) Food I 12 ounces,
Food II 16 ounces,
Food III 10 ounces
​
D) Food I 10 ounces,
Food II 16 ounces,
Food III 12 ounces
​
E) Food I 6 ounces,
Food II 13 ounces,
Food III 10 ounces
​
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method. <div style=padding-top: 35px>
سؤال
The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $.30, the adult fare is $.65, and the total revenue from the fares in the morning shift is 480, how many children and how many adults rode the bus during the morning shift? ​

A) 620 children and 280 adults
B) 600 children and 300 adults
C) 320 children and 580 adults
D) 300 children and 620 adults
E) 300 children and 600 adults
سؤال
A theater has a seating capacity of 450 and charges $2 for children, $3 for students, and $5 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $1,550. How many children attended the show? ​

A) 300 children
B) 190 children
C) 10 children
D) 390 children
E) 100 children
سؤال
Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​

A) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
B) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
C) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
D) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
E) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E) <div style=padding-top: 35px>
سؤال
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method. <div style=padding-top: 35px>
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Deck 2: Systems of Linear Equations and Matrices
1
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution ​

A) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution
B) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution
C) infinitely many solutions <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution
D) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) infinitely many solutions D) one and only one solution E) no solution
E) no solution
one and only one solution one and only one solution
2
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
D) No solution
No solution
3
Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.

A) <strong>Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.</strong> A) B) C) D)
B) <strong>Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.</strong> A) B) C) D)
C) <strong>Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.</strong> A) B) C) D)
D) <strong>Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.</strong> A) B) C) D)
4
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution ​

A) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
B) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
C) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
D) infinitely many solutions <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
E) no solution
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5
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
D) No solution
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6
Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of nitrogen, <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of phosphate, and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of potassium. A 100-lb bag of grade-B fertilizer contains <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of nitrogen and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of nitrogen, <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of phosphate, and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of nitrogen, <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of phosphate, and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution lb of potassium are available and all the nutrients are used?

A) <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution , <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution 100-lb bags correspondingly
B) <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution , <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution 100-lb bags correspondingly
C) <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution , <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution 100-lb bags correspondingly
D) <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution , <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution and <strong>Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used?</strong> A) , and 100-lb bags correspondingly B) , and 100-lb bags correspondingly C) , and 100-lb bags correspondingly D) , and 100-lb bags correspondingly E) the problem has no solution 100-lb bags correspondingly
E) the problem has no solution
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7
Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.

A) <strong>Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.</strong> A) B) C) D)
B) <strong>Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.</strong> A) B) C) D)
C) <strong>Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.</strong> A) B) C) D)
D) <strong>Formulate but do not solve the problem. The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $4.00/lb. If the blended coffee sells for $3.70/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100lb.) Let x be the weight of coffee with price $3.00/lb.</strong> A) B) C) D)
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Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) ​

A) One and only one solution;( <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) , <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) )
B) No solution
C) One and only one solution; ( <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) , <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) )
D) Infinitely many solutions
E) One and only one solution; ( <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) , <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) One and only one solution;( , ) B) No solution C) One and only one solution; ( , ) D) Infinitely many solutions E) One and only one solution; ( , ) )
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9
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution ​

A) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
B) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
C) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
D) infinitely many solutions <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
E) no solution
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10
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
D) No solution
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11
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
D) No solution
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12
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
D) No solution
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13
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution ​

A) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
B) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
C) one and only one solution <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
D) infinitely many solutions <strong>Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​ ​</strong> A) one and only one solution B) one and only one solution C) one and only one solution D) infinitely many solutions E) no solution
E) no solution
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14
Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.

A) <strong>Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.</strong> A) B) C) D)
B) <strong>Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.</strong> A) B) C) D)
C) <strong>Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.</strong> A) B) C) D)
D) <strong>Formulate but do not solve the problem. The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $0.25, the adult fare is $0.75, and the total revenue from the fares in the morning shift is $475, how many children and how many adults rode the bus during the morning shift? Let x be the number of children.</strong> A) B) C) D)
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15
Determine the value of k for which the system of linear equations has no solution. ​ <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E) ​

A) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E)
B) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E)
C) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E)
D) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E)
E) <strong>Determine the value of k for which the system of linear equations has no solution. ​ ​</strong> A) B) C) D) E)
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16
Formulate but do not solve the problem. ​
The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn.
​

A) <strong>Formulate but do not solve the problem. ​ The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn. ​</strong> A) ​ B) ​ C) ​ D) ​ ​
B) <strong>Formulate but do not solve the problem. ​ The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn. ​</strong> A) ​ B) ​ C) ​ D) ​ ​
C) <strong>Formulate but do not solve the problem. ​ The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn. ​</strong> A) ​ B) ​ C) ​ D) ​ ​
D) <strong>Formulate but do not solve the problem. ​ The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn. ​</strong> A) ​ B) ​ C) ​ D) ​ ​
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17
Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are ​

A) <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are . The solutions are <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are
B) <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are . The solutions are <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are
C) <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are . The solutions are <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are
D) <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are . The solutions are <strong>Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. ​ ​</strong> A) . The solutions are B) . The solutions are C) . The solutions are D) . The solutions are
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18
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
D) No solution
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19
Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E) units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E) times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.

A) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E)
B) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E)
C) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E)
D) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E)
E) <strong>Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.</strong> A) B) C) D) E)
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20
Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.

A) <strong>Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.</strong> A) B) C) D)
B) <strong>Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.</strong> A) B) C) D)
C) <strong>Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.</strong> A) B) C) D)
D) <strong>Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.</strong> A) B) C) D)
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21
Solve the linear system of equations. If the system is inconsistent, indicate this.
​ Solve the linear system of equations. If the system is inconsistent, indicate this. ​
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22
Formulate but do not solve the problem.
​
The Johnson Farm has 600 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $46 and $23/acre, respectively. Jacob Johnson has $18,400 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant?
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23
Formulate but do not solve the problem. ​
A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks.
​

A) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E)
B) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E)
C) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E)
D) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E)
E) <strong>Formulate but do not solve the problem. ​ A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks. ​</strong> A) B) C) D) E)
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24
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.
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25
Solve the linear system of equations. If the system is inconsistent, indicate this. Solve the linear system of equations. If the system is inconsistent, indicate this.
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26
Solve the linear system of equations. If the system is inconsistent, indicate this. Solve the linear system of equations. If the system is inconsistent, indicate this.
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27
Solve the linear system of equations. If the system is inconsistent, indicate this.
​ Solve the linear system of equations. If the system is inconsistent, indicate this. ​
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28
Solve the linear system of equations. If the system is inconsistent, indicate this. Solve the linear system of equations. If the system is inconsistent, indicate this.
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29
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.
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30
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.
​ Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. ​
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31
Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.

A) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E)
B) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E)
C) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E)
D) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E)
E) <strong>Formulate but do not solve the problem. The annual returns on Sid Carrington's three investments amounted to $28,000: 6% on a saving account, 10% on mutual funds and 16% on bonds. The amount of Sid's investment in bouds was twice the amount of his investment in the savings account and the interest earned from his investment in bounds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. Let x be the money invested in saving account, y be the money investedr in mutual funds and z be the money invested in bonds.</strong> A) B) C) D) E)
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32
Determine the value of k for which the system of linear equations has no solution.
​ Determine the value of k for which the system of linear equations has no solution. ​ ​ k = __________ ​
k = __________
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33
Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show?
Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.

A) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E)
B) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E)
C) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E)
D) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E)
E) <strong>Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show? Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.</strong> A) B) C) D) E)
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34
Solve the linear system of equations. If the system is inconsistent, indicate this.
​ Solve the linear system of equations. If the system is inconsistent, indicate this. ​
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35
Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.

A) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E)
B) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E)
C) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E)
D) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E)
E) <strong>Formulate but do not solve the problem. The management of Hartman Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full size cars. Compacts cost $13,202 each, intermediate-size cars cost $28,827 each, and full-size cars cost $36,854 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 128, determine how many cars of each type will be purchased.(Assume that the entire budget will be used.) Let x be the number of compact, y be the number of intermediate-size cars, z be the number of full-size cars.</strong> A) B) C) D) E)
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36
Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k. Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k.
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37
Solve the linear system of equations ​ <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution ​

A) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
B) Unique solution: <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
C) Infinitely many solutions; <strong>Solve the linear system of equations ​ ​</strong> A) Unique solution: B) Unique solution: C) Infinitely many solutions; D) No solution
D) No solution
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38
Solve the linear system of equations. If the system is inconsistent, indicate this. Solve the linear system of equations. If the system is inconsistent, indicate this.
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39
A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are parallel.

A) true
B) false
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40
Formulate but do not solve the problem.
​
Michael Perez has a total of $1,500 on deposit with two savings institutions. One pays interest at the rate of 8%/year, whereas the other pays interest at the rate of 5%/year. If Michael earned a total of $96 in interest during a single year, how much does he have on deposit in each institution?
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41
Formulate but do not solve the problem.
​
The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $1.50/lb. If the blended coffee sells for $2.10/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.)
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42
A dietitian wishes to plan a meal around three foods. The percentage of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods is summarized in the accompanying table. A dietitian wishes to plan a meal around three foods. The percentage of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods is summarized in the accompanying table. Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100% of each). __________ ounces of Food I __________ ounces of Food II __________ ounces of Food III Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100% of each).
__________ ounces of Food I
__________ ounces of Food II
__________ ounces of Food III
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43
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) ( 23, 7 ) B) ( 33, 7 ) C) ( 28, -12 ) D) ( -7, 28 ) E) ( 28, -7 )

A) ( 23, 7 )
B) ( 33, 7 )
C) ( 28, -12 )
D) ( -7, 28 )
E) ( 28, -7 )
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44
Determine whether the statement is true or false.
​
A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are nonparallel.
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45
Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of nitrogen, Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of phosphate, and Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of potassium. A 100-lb bag of grade-B fertilizer contains Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of nitrogen and Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of nitrogen, Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of phosphate, and Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of nitrogen, Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of phosphate, and Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. A 100-lb bag of grade-B fertilizer contains lb of nitrogen and lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains lb of nitrogen, lb of phosphate, and lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if lb of nitrogen, lb of phosphate, and lb of potassium are available and all the nutrients are used? ​ grade-A fertilizer: __________ 100-lb bags ​ grade-B fertilizer: __________ 100-lb bags ​ grade-C fertilizer: __________ 100-lb bags lb of potassium are available and all the nutrients are used?
​
grade-A fertilizer: __________ 100-lb bags
​
grade-B fertilizer: __________ 100-lb bags
​
grade-C fertilizer: __________ 100-lb bags
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46
Formulate but do not solve the problem.
​
The total number of passengers riding a certain city bus during the morning shift is 1,000. If the child's fare is $0.65, the adult fare is $0.35, and the total revenue from the fares in the morning shift is $440, how many children and how many adults rode the bus during the morning shift?
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47
Formulate but do not solve the problem.
​
Kelly Fisher has a total of $32,000 invested in two municipal bonds that have yields of $5% and $6% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,740, how much does she have invested in each bond?
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48
Pivot the system about the bolded element. ​ <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E) ​

A) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E)
B) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E)
C) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E)
D) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E)
E) <strong>Pivot the system about the bolded element. ​ ​</strong> A) B) C) D) E)
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49
Solve the system of linear equations using the Gauss-Jordan elimination <strong>Solve the system of linear equations using the Gauss-Jordan elimination </strong> A) ( 5, -18, -12 ) B) ( -21, 5, 12 ) C) ( 12, -18, -5 ) D) ( 18, 5, 12 ) E) ( 18, -5, -12 )

A) ( 5, -18, -12 )
B) ( -21, 5, 12 )
C) ( 12, -18, -5 )
D) ( 18, 5, 12 )
E) ( 18, -5, -12 )
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50
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is not in row-reduced form. B) The matrix is in row-reduced form.

A) The matrix is not in row-reduced form.
B) The matrix is in row-reduced form.
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51
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is in row-reduced form. B) The matrix is not in row-reduced form.

A) The matrix is in row-reduced form.
B) The matrix is not in row-reduced form.
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52
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is not in row-reduced form. B) The matrix is in row-reduced form.

A) The matrix is not in row-reduced form.
B) The matrix is in row-reduced form.
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53
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) ( 5, -2, -3 ) B) ( 3, -2, -5 ) C) ( -5, 3, 5 ) D) ( 2, -3, 5 ) E) ( 2, 3, 5 )

A) ( 5, -2, -3 )
B) ( 3, -2, -5 )
C) ( -5, 3, 5 )
D) ( 2, -3, 5 )
E) ( 2, 3, 5 )
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54
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) ( 8, -3 ) B) ( 7, -2 ) C) ( 2, -7 ) D) ( -7, 2 ) E) ( -8, -2 )

A) ( 8, -3 )
B) ( 7, -2 )
C) ( 2, -7 )
D) ( -7, 2 )
E) ( -8, -2 )
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55
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) ( 2, -10, -12 ) B) ( 12, -10, -2 ) C) ( -15, 12, 2 ) D) ( 10, 12, -2 ) E) ( 10, 12, 2 )

A) ( 2, -10, -12 )
B) ( 12, -10, -2 )
C) ( -15, 12, 2 )
D) ( 10, 12, -2 )
E) ( 10, 12, 2 )
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56
Write the augmented matrix corresponding to the given system of equations. <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E)

A) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E)
B) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E)
C) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E)
D) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E)
E) <strong>Write the augmented matrix corresponding to the given system of equations. </strong> A) B) C) D) E)
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57
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is not in row-reduced form. B) The matrix is in row-reduced form.

A) The matrix is not in row-reduced form.
B) The matrix is in row-reduced form.
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58
Solve the system of linear equations, using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z =

A) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = , y = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = , z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z =
B) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = , y = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = , z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z =
C) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = , y = 0, z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z =
D) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = , y = 0, z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z =
E) x = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z = , y = 0, z = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x = , y = , z = B) x = , y = , z = C) x = , y = 0, z = D) x = , y = 0, z = E) x = , y = 0, z =
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59
Indicate whether the matrix is in row-reduced form. <strong>Indicate whether the matrix is in row-reduced form. </strong> A) The matrix is in row-reduced form. B) The matrix is not in row-reduced form.

A) The matrix is in row-reduced form.
B) The matrix is not in row-reduced form.
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60
Solve the system of linear equations using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E)

A) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E)
B) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E)
C) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E)
D) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E)
E) <strong>Solve the system of linear equations using the Gauss-Jordan elimination method. </strong> A) B) C) D) E)
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61
The annual interest on Sid Carrington's three investments amounted to $35,100: 6% on a savings account, 9% on mutual funds, and 12% on bonds. If the amount of Sid's investment in bonds was triple the amount of his investment in the savings account, and the interest earned from his investment in bonds was equal to the dividends he received from his investment in mutual funds, find how much money he placed in each type of investment. ​

A) $180,000 in a savings account, $45,000 in mutual funds, $135,000 in bonds
B) $135,000 in a savings account, $180,000 in mutual funds, $45,000 in bonds
C) $180,000 in a savings account, $135,000 in mutual funds, $45,000 in bonds
D) $45,000 in a savings account, $180,000 in mutual funds, $135,000 in bonds
E) $45,000 in a savings account, $135,000 in mutual funds, $180,000 in bonds
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62
Solve the system of linear equations, using the Gauss-Jordan elimination method. <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0

A) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x3 = 0
B) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x3 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0
C) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x3 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0
D) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x3 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0
E) x1 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x2 = <strong>Solve the system of linear equations, using the Gauss-Jordan elimination method. </strong> A) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 B) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = C) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = D) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = E) x<sub>1</sub> = , x<sub>2</sub> = , x<sub>3</sub> = 0 , x3 = 0
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63
The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $2.50/lb. If the blended coffee sells for $2.90/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.) ​

A) 20 lb of $3.00/lb coffee and 80 lb of $2.50/lb coffee
B) 75 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee
C) 80 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee
D) 80 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee
E) 85 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee
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64
A theater has a seating capacity of 750 and charges $2 for children, $4 for students, and $5 for adults. At a certain screening with full attendance, there were one-fourth as many adults as children and students combined. The receipts totaled $2,150. How many children attended the show?
​
__________ children
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65
An executive of Trident Communications recently traveled to London, Paris, and Rome. He paid $170, $230, and $150/night for lodging in London, Paris, and Rome, respectively, and his hotel bills totaled $4,240. He spent $110, $130, and $100/day for his meals in London, Paris, and Rome, respectively, and his expenses for meals totaled $2,670. If he spent as many days in London as he did in Paris and Rome combined, how many days did he stay in each city? ​

A) 14 days in London, 5 days in Paris, 9 days in Rome
B) 12 days in London, 5 days in Paris, 7 days in Rome
C) 16 days in London, 7 days in Paris, 9 days in Rome
D) 7 days in London, 5 days in Paris, 12 days in Rome
E) 14 days in London, 7 days in Paris, 7 days in Rome
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66
Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​

A) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E)
B) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E)
C) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E)
D) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E)
E) <strong>Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​</strong> A) B) C) D) E)
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67
The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $38 and $30/acre, respectively. Jacob Johnson has $16,600 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? ​

A) 250 acres of corn and 300 acres of wheat
B) 300 acres of corn and 200 acres of wheat
C) 450 acres of corn and 50 acres of wheat
D) 200 acres of corn and 300 acres of wheat
E) 200 acres of corn and 350 acres of wheat
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68
Write the system of equations corresponding to the given augmented matrix.
​ Write the system of equations corresponding to the given augmented matrix. ​
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69
Write the augmented matrix corresponding to the given system of equations. Write the augmented matrix corresponding to the given system of equations.
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70
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method.
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71
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method.
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72
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method.
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73
Write the augmented matrix corresponding to the given system of equations. Write the augmented matrix corresponding to the given system of equations.
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74
Solve the system of linear equations, using the Gauss-Jordan elimination method. Solve the system of linear equations, using the Gauss-Jordan elimination method. x = __________ y =__________ z =__________
x = __________
y =__________
z =__________
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75
A dietitian wishes to plan a meal around three foods. The percent of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods is summarized in the table. Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100% of each). <strong>A dietitian wishes to plan a meal around three foods. The percent of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods is summarized in the table. Determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100% of each). ​</strong> A) Food I 10 ounces, Food II 5 ounces, Food III 6 ounces ​ B) Food I 4 ounces, Food II 2 ounces, Food III 5 ounces ​ C) Food I 12 ounces, Food II 16 ounces, Food III 10 ounces ​ D) Food I 10 ounces, Food II 16 ounces, Food III 12 ounces ​ E) Food I 6 ounces, Food II 13 ounces, Food III 10 ounces ​ ​

A) Food I 10 ounces,
Food II 5 ounces,
Food III 6 ounces
​
B) Food I 4 ounces,
Food II 2 ounces,
Food III 5 ounces
​
C) Food I 12 ounces,
Food II 16 ounces,
Food III 10 ounces
​
D) Food I 10 ounces,
Food II 16 ounces,
Food III 12 ounces
​
E) Food I 6 ounces,
Food II 13 ounces,
Food III 10 ounces
​
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76
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method.
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77
The total number of passengers riding a certain city bus during the morning shift is 900. If the child's fare is $.30, the adult fare is $.65, and the total revenue from the fares in the morning shift is 480, how many children and how many adults rode the bus during the morning shift? ​

A) 620 children and 280 adults
B) 600 children and 300 adults
C) 320 children and 580 adults
D) 300 children and 620 adults
E) 300 children and 600 adults
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78
A theater has a seating capacity of 450 and charges $2 for children, $3 for students, and $5 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $1,550. How many children attended the show? ​

A) 300 children
B) 190 children
C) 10 children
D) 390 children
E) 100 children
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79
Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​

A) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E)
B) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E)
C) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E)
D) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E)
E) <strong>Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​</strong> A) B) C) D) E)
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80
Solve the system of linear equations using the Gauss-Jordan elimination method. Solve the system of linear equations using the Gauss-Jordan elimination method.
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