Deck 5: Systems of Equations and Inequalities

Question 1

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( 6 , - 3 ) \\2 x - y = 9 \\4 x - 2 y = 18\end{array}$$

A) not a solution
B) solution

Answer 1

A

Question 2

Solve the system of equations by the substitution method.
$$\begin{array} { l } y = 3 x + 9 \\y = 8 x + 8\end{array}$$

A) $\left\{ \left( \frac { 1 } { 5 } , \frac { 48 } { 5 } \right) \right\}$
B) $\left\{ \left( \frac { 48 } { 5 } , \frac { 1 } { 5 } \right) \right\}$
C) $\{ ( 1,12 ) \}$
D) $\varnothing$

Answer 2

A

Question 3

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( 5 , - 1 ) \\3 x + y = 14 \\2 x + 3 y = 7\end{array}$$

A) solution
B) not a solution

Answer 3

A

Question 4

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( - 1,5 ) \\4 x = 9 - y \\2 x = 22 - 4 y\end{array}$$

A) not a solution
B) solution

Question 5

Solve the system of equations by the substitution method.
$$\begin{array} { l } 6 x + y = - 7 \\3 x - 5 y = - 9\end{array}$$

A) $\left. \left\{ - \frac { 4 } { 3 } , 1 \right] \right\}$
B) $\{ ( 1,9 ) \}$
C) $\left\{ \left[ - 5 , \frac { 6 } { 5 } \right\} \right\}$
D) $\left\{ \left[ - \frac { 1 } { 3 } , - 5 \right\} \right\}$

Question 6

Solve the system of equations by the substitution method.
$$\begin{array} { r } - 4 \mathrm { x } - 2 \mathrm { y } = 22 \\\mathrm { x } = 5 \mathrm { y }\end{array}$$

A) $\{ ( - 5 , - 1 ) \}$
B) $\{ ( - 1 , - 5 ) \}$
C) $\{ ( - 5,1 ) \}$
D) $\{ ( - 4 , - 1 ) \}$

Question 7

Solve the system of equations by the substitution method.
$$\begin{array} { l } 5 x - 6 y = 2 - 5 x \\2 x + 6 y = x + 5 y + - 3\end{array}$$

A) $\{ ( - 1 , - 2 ) \}$
B) $\{ ( - 1,2 ) \}$
C) $\{ ( 0,2 ) \}$
D) $\left\{ \left[ \frac { 1 } { 5 } , 0 \right\} \right\}$

Question 8

Solve the system of equations by the substitution method.
$$\begin{aligned}- 2 x - 4 y & = 16 \\x - 2 y & = 0\end{aligned}$$
$$x - 2 y = 0$$

A) $\{ ( - 4 , - 2 ) \}$
B) $\{ ( - 2 , - 4 ) \}$
C) $\{ ( - 4,2 ) \}$
D) $\{ ( - 3 , - 2 ) \}$

Question 9

Solve the system of equations by the substitution method.
$$\begin{array} { l } y = \frac { 1 } { 6 } x - 2 \\y = \frac { 2 } { 5 } x + 12\end{array}$$

A) $\{ ( - 60 , - 12 ) \}$
B) $\{ ( - 60,12 ) \}$
C) $\{ ( 12,0 ) \}$
D) $\left\{ \left( - \frac { 59 } { 6 } , - \frac { 149 } { 7 } \right) \right\}$

Question 10

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( 6 , - 6 ) \\2 x - y = 6 \\4 x + 2 y = 12\end{array}$$

A) not a solution
B) solution

Question 11

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( 3 , - 2 ) \\x + y = 1 \\x - y = 5\end{array}$$

A) solution
B) not a solution

Question 12

Solve the system of equations by the substitution method.
$$\begin{aligned}y & = 5 x + 4 \\5 y - 15 x & = 30\end{aligned}$$

A) $\{ ( 1,9 ) \}$
B) $\{ ( 9,1 ) \}$
C) $\{ ( - 1,9 ) \}$
D) $\varnothing$

Question 13

Solve the system of equations by the substitution method.
$$\begin{array} { r } x - 3 y = - 30 \\- 5 x - 4 y = - 2\end{array}$$

A) $\{ ( - 6,8 ) \}$
B) $\{ ( - 7,9 ) \}$
C) $\{ ( 6,9 ) \}$
D) $\varnothing$

Question 14

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( 1 , - 6 ) \\3 x + y = 9 \\4 x + 3 y = 22\end{array}$$

A) not a solution
B) solution

Question 15

Solve the system of equations by the substitution method.
$- 4 x + 7 y = 59$ $2 x - 5 y = - 43$

A) $\{ ( 1,9 ) \}$
B) $\{ ( 0,10 ) \}$
C) $\{ ( 1,10 ) \}$
D) $\varnothing$

Question 16

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( 2,5 ) \\2 x = 9 - y \\3 x = 16 - 2 y\end{array}$$

A) solution
B) not a solution

Question 17

Solve the system of equations by the substitution method.
$$\begin{aligned}x + y & = - 9 \\y & = - 4 x\end{aligned}$$

A) $\{ ( 3 , - 12 ) \}$
B) $\{ ( 3,12 ) \}$
C) $\{ ( - 3 , - 12 ) \}$
D) $\{ ( - 3,12 ) \}$

Question 18

Solve the system by the addition method.
$x + y = - 1$ $x - y = 14$

A) $\{ ( 6.5 , - 7.5 ) \}$
B) $\{ ( 6.5,7.5 ) \}$
C) $\{ ( 1 , - 7.5 ) \}$
D) $\{ ( 1,6.5 ) \}$

Question 19

Determine whether the given ordered pair is a solution of the system.
$$\begin{array} { l } ( - 2 , - 5 ) \\x + y = - 3 \\x - y = 7\end{array}$$

A) not a solution
B) solution

Question 20

Solve the system of equations by the substitution method.
$$2 y = x + 8$$
$2 x + 4 y = 0$

A) $\{ ( - 4,2 ) \}$
В) $\{ ( 2 , - 4 ) \}$
C) $\{ ( - 4 , - 2 ) \}$
D) $\{ ( 4,1 ) \}$

Question 21

Solve the system by the addition method.
$$\begin{array} { l } 2 y = - 22 - 7 x \\2 x = 8 - 2 y\end{array}$$

A) $\{ ( - 6,10 ) \}$
B) $\{ ( 2 , - 10 ) \}$
C) $\{ ( 7 , - 10 ) \}$
D) $\varnothing$

Question 22

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } 3 y = 21 - 4 x \\2 x = 27 - 3 y\end{array}$$

A) $\{ ( - 3,11 ) \}$
B) $\{ ( 3 , - 11 ) \}$
C) $\{ ( x , y ) \mid 4 x + 3 y = 21 \}$
D) $\varnothing$

Question 23

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { r } x + 8 y = 37 \\5 x + 7 y = 20\end{array}$$

A) $\{ ( - 3,5 ) \}$
B) $\{ ( - 4,6 ) \}$
C) $\{ ( x , y ) \mid x + 8 y = 37 \}$
D) $\varnothing$

Question 24

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } x + y = 7 \\x + y = 3\end{array}$$

A) $\{ ( 0,10 ) \}$
B) $\{ ( 7,3 ) \}$
C) $\{ ( x , y ) \mid x + y = 7 \}$
D) $\varnothing$

Question 25

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } 2 x + y = 7 \\4 x + 2 y = 14\end{array}$$

A) $\{ ( 0,7 ) \}$
B) $\{ ( 5 , - 3 ) \}$
C) $\{ ( x , y ) \mid 2 x + y = 7 \}$
D) $\varnothing$

Question 26

Solve the system by the addition method.
$$\begin{array} { l } 6 x + 5 y = 95 \\6 x + 2 y = 110\end{array}$$

A) $\{ ( 20 , - 5 ) \}$
B) $\{ ( - 20,6 ) \}$
C) $\{ ( - 20,5 ) \}$
D) $\{ ( - 5,20 ) \}$

Question 27

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } x + y = - 9 \\x - y = 12\end{array}$$

A) $\{ ( 1.5 , - 10.5 ) \}$
B) $\{ ( 1.5,10.5 ) \}$
C) $\{ ( x , y ) \mid x + y = - 9 \}$
D) $\varnothing$

Question 28

Solve the system by the addition method.
$$9 x - 7 y = - 61$$
$- 3 x - 2 y = 16$

A) $\{ ( - 6,1 ) \}$
B) $\{ ( - 7,2 ) \}$
C) $\{ ( - 6,2 ) \}$
D) $\varnothing$

Question 29

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } y = 6 x + 1 \\- 24 x + 4 y = 4\end{array}$$

A) $\{ ( 0,1 ) \}$
B) $\{ ( 0,0 ) \}$
C) $\{ ( x , y ) \mid - 6 x + y = 1 \}$
D) $\varnothing$

Question 30

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } y = 19 - 4 x \\4 x + y = 43\end{array}$$

A) $\{ ( 9,15 ) \}$
B) $\{ ( 12,7 ) \}$
C) $\{ ( x , y ) \mid 4 x + y = 19 \}$
D) $\varnothing$

Question 31

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } y = 10 - 4 x \\16 x + 4 y = 40\end{array}$$

A) $\{ ( 0,10 ) \}$
B) $\{ ( 5 , - 10 ) \}$
C) $\{ ( x , y ) \mid 4 x + y = 10 \}$
D) $\varnothing$

Question 32

Solve the system by the addition method.
$$7 x + 9 y = 9$$
$9 x - 3 y = - 3$

A) $\{ ( 0,1 ) \}$
B) $\{ ( 1,0 ) \}$
C) $\{ ( 1,1 ) \}$
D) $\{ ( 0,0 ) \}$

Question 33

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } 2 \mathrm { x } + \mathrm { y } = 7 \\2 \mathrm { y } = 14 - 4 \mathrm { x }\end{array}$$

A) $\left\{ \left[ \frac { 7 } { 2 } , 0 \right\} \right\}$
B) $\{ ( 0,7 ) \}$
C) $\{ ( x , y ) \mid 2 x + y = 7 \}$
D) $\varnothing$

Question 34

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$x - 4 y = 3$$
$- 5 x + 20 y = - 15$

A) $\{ ( 3,0 ) \}$
B) $\{ ( 0,0 ) \}$
C) $\{ ( x , y ) \mid x - 4 y = 3 \}$
D) $\varnothing$

Question 35

Solve the system by the addition method.
$$\begin{array} { l } - 2 x - 5 y = - 17 \\5 x - 3 y = - 4\end{array}$$

A) $\{ ( 1,3 ) \}$
B) $\{ ( - 1 , - 3 ) \}$
C) $\{ ( 1 , - 3 ) \}$
D) $\{ ( - 1,3 ) \}$

Question 36

Solve the system by the addition method.
$$\begin{aligned}x + 6 y & = 11 \\4 x + 5 y & = - 13\end{aligned}$$

A) $\{ ( - 7,3 ) \}$
B) $\{ ( - 8,4 ) \}$
C) $\{ ( 7,4 ) \}$
D) $\varnothing$

Question 37

Solve the system by the addition method.
$$\begin{array} { c } 2 \mathrm { x } + 10 \mathrm { y } = - 56 \\10 \mathrm { x } + 2 \mathrm { y } = 56\end{array}$$

A) $\{ ( 7 , - 7 ) \}$
B) $\{ ( - 7,7 ) \}$
C) $\{ ( 10 , - 10 ) \}$
D) $\{ ( - 2,7 ) \}$

Question 38

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } 5 x - 6 y = 2 \\- 20 x + 24 y = - 4\end{array}$$

A) $\{ ( 4,2 ) \}$
B) $\left\{ \left( \frac { 15 } { 2 } , - 9 \right) \right\}$
C) $\{ ( x , y ) \mid 5 x - 6 y = 2 \}$
D) $\varnothing$

Question 39

Solve the system by the addition method.
$$\begin{array} { r } 5 x + 2 y = - - 1 \\- 5 x - 5 y = 5\end{array}$$

A) $\{ ( 1 , - 2 ) \}$
B) $\{ ( - 1,2 ) \}$
C) $\{ ( - 1 , - 2 ) \}$
D) $\varnothing$

Question 40

Solve the system by the addition method.
$$\begin{array} { l } - 6 x + y = 10 \\9 x + 4 y = - 4\end{array}$$

A) $\left\{ \left( - \frac { 4 } { 3 } , 2 \right] \right\}$
B) $\{ ( 1 , - 6 ) \}$
C) $\left\{ \left( 4 , - \frac { 19 } { 4 } \right) \right\}$
D) $\left\{ \left( - \frac { 1 } { 3 } , 8 \right) \right\}$

Question 41

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.

Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

A)750 binoculars
B)2250 binoculars
C)1500 binoculars
D)2700 binoculars

Question 42

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\frac { x } { 3 } + \frac { y } { 3 } = 2$$
$\mathrm { x } - \mathrm { y } = 4$

A) $\{ ( 5,1 ) \}$
B) $\{ ( 4,2 ) \}$
C) $\{ ( x , y ) \mid x - y = 4 \}$
D) $\varnothing$

Question 43

Solve the problem.
One number is 2 less than a second number. Twice the second number is 8 less than 3 times the first. Find the two numbers.

A)12 and 14
B)11 and 13
C)13 and 15
D)-14 and -12

Question 44

Solve the problem.
Steve invests in a circus production. The cost includes an overhead of $54,000, plus production costs of $4000 per performance. A sold-out performance brings in $13,000. Determine the dollar amount coming
In and going out at the break-even point.

A)$78,000
B)$24,000
C)$6
D)$41,294

Question 45

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } 2 x - 7 y = 5 \\- 6 x + 21 y = - 20\end{array}$$

A) $\left\{ \left( \frac { 4 } { 15 } , - \frac { 14 } { 15 } \right) \right\}$
B) $\{ ( 3,4 ) \}$
C) $\{ ( x , y ) \mid 2 x - 7 y = 5 \}$
D) $\varnothing$

Question 46

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.

Is there a profit when 947 binoculars are produced?

A)Yes
B)No

Question 47

Solve the problem.
Steve invests in a circus production. The cost includes an overhead of $56,000, plus production costs of $5000 per performance. A sold-out performance brings in $13,000. Let x represent the number of sold-out
Performances and write the cost function, C and revenue function, R. A) $C ( x ) = 56,000 + 5000 x$
$R ( x ) = 13,000 x$
B) $C ( x ) = 56,000 + 13,000 x$
$R ( x ) = 5000 x$
C) $C ( x ) = 5000 x$
$R ( x ) = 56,000 + 13,000 x$
D) $C ( x ) = 56,000 x + 5000$
$R ( x ) = 13,000 x$

Question 48

Solve the problem.
One number is 6 less than a second number. Twice the second number is 27 more than 3 times the first. Find the two numbers.

A)-15 and -9
B)-16 and -10
C)-14 and -8
D)9 and 15

Question 49

Solve the problem.
Steve invests in a circus production. The cost includes an overhead of $36,000, plus production costs of $6000 per performance. A sold-out performance brings in $9000. Determine the number of sold-out
Performances, x, needed to break even.

A)12 performances
B)13 performances
C)14 performances
D)4 performances

Question 50

Solve the problem.
An-Mei owns a business making and selling jackets. She has a fixed cost of $4050. It costs $69 to produce each jacket. The selling price is $96 per jacket. Let x represent the number of jackets produced and sold
And write the cost function, C, and revenue function, R. A) $C ( x ) = 69 x + 4050$
$R ( x ) = 96 x$
B) $C ( x ) = 69 + 96 x$
$R ( x ) = 4050 x$
C) $C ( x ) = 69 + 4050 x$
$R ( x ) = 96$
D) $C ( x ) = 69 x + 4050 x$
$R ( x ) = 96 x$

Question 51

Solve the problem.
Two cars leave a city and head in the same direction. After 5 hours, the faster car is 40 miles ahead of the slower car. The slower car has traveled 240 miles. Find the speeds of the two cars.

A)48 mph and 56 mph
B)50 mph and 58 mph
C)80 mph and 88 mph
D)40 mph and 48 mph

Question 52

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.

How many binoculars must be produced and sold for the company to break even?

A)750 binoculars
B)2250 binoculars
C)1500 binoculars
D)2700 binoculars

Question 53

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } y = \frac { 1 } { 2 } x + 6 \\x - 2 y = - 12\end{array}$$

A) $\{ ( - 12,0 ) \}$
B) $\{ ( 0,6 ) \}$
C) $\{ ( x , y ) \mid x - 2 y = - 12 \}$
D) $\varnothing$

Question 54

Solve the problem.
The sum of two numbers is 8. If one number is subtracted from the other, their difference is 2. Find the numbers.

A)5, 3
B)5, -3
C)-5, 3
D)6, 2

Question 55

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.

At the break-even point both cost and revenue are what?

A)$2250
B)$750
C)$1500
D)$2700

Question 56

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.

What is the profit when 996 binoculars are produced?

A)$492
B)$3492
C)$2484
D)$5484

Question 57

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.

Is there a profit when 323 binoculars are produced?

A)No
B)Yes

Question 58

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.

Use the revenue and cost functions to write the profit function from producing and selling x binoculars.

A)P(x)= 2x - 1500
B)P(x)= 2x + 1500
C)P(x)= 4x + 1500
D)P(x)= 4x - 1500

Question 59

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells
binoculars. Use the information in the figure to answer the question.

More than how many binoculars must be produced and sold for the company to have a profit gain?

A)750 binoculars
B)2250 binoculars
C)1500 binoculars
D)2700 binoculars

Question 60

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
$$\begin{array} { l } \frac { x } { 3 } + \frac { y } { 6 } = 1 \\\frac { x } { 2 } - \frac { y } { 4 } = 0\end{array}$$

A) $\left\{ \left( \frac { 3 } { 2 } , 3 \right) \right\}$
B) $\left\{ \left( 3 , \frac { 3 } { 2 } \right) \right\}$
C) $\left\{ ( x , y ) \mid \frac { x } { 3 } + \frac { y } { 6 } = 1 \right\}$
D) $\varnothing$

Question 61

Solve the problem.
A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 11 inches longer than the width. Find the width.

A)9 inches
B)20 inches
C)31 inches
D)29 inches

Question 62

Solve the problem.
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 860 calories. Three servings of ice cream and two servings of blueberry pie provides 1300 calories. Find the
Caloric content of each item. A) Serving of ice cream: 220 calories
Serving of blueberry pie: 320 calories
B) Serving of ice cream: 320 calories
Serving of blueberry pie: 220 calories
C) Serving of ice cream: 196 calories
Serving of blueberry pie: 332 calories
D) Serving of ice cream: 236 calories
Serving of blueberry pie: 312 calories

Question 63

Solve the problem.
As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The weekly supply and demand models
For a certain type of television are as follows: Demand: $\mathrm { N } = - 6 \mathrm { p } + 730$
Supply: $\quad N = 2.4 p$
where $\mathrm { p }$ is the price in dollars per television.
Find the price at which supply and demand are equal. At this price, how many televisions can be supplied and sold each week?

A) $\$ 86.90 ; 209$
B) $\$ 202.78 ; 487$
C) $\$ 301.67 ; 724$
D) $\$ 86.90 ; 230$

Question 64

Solve the problem.
Julie and Eric row their boat (at a constant speed)21 miles downstream for 3 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 7 hours. Find the rate of the current.

A)2 mph
B)5 mph
C)3 mph
D)1.5 mph

Question 65

Solve the problem.
You invested $34,200 and started a business selling vases. Supplies cost $10 per vase and you are selling each vase for $29. Determine the number of vases, x, that must be produced and sold to break even.

A)1800 units
B)1801 units
C)1802 units
D)713 units

Question 66

Solve the problem.
A twin-engined aircraft can fly 952 miles from city A to city B in 4 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?

A)51 mph
B)34 mph
C)68 mph
D)85 mph

Question 67

Determine if the given ordered triple is a solution of the system.
$$\begin{array} { c } ( - 2,5 , - 5 ) \\x + y + z = - 2 \\x - y + 5 z = - 32 \\2 x + y + z = - 4\end{array}$$

A) solution
B) not a solution

Question 68

Solve the problem.
In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing.
Let x represent the number of years since 1990 and y represent the percentage of women in Milton Lake
Who smoke. The graph of y against x includes the data points (0, 16.6)and (13, 19.98). Let x represent the
Number of years since 1990 and y represent the percentage of men in Milton Lake who smoke. The graph
Of y against x includes the data points (0, 28.8)and (14, 25.86).
Determine when the percentage of women who smoke will be the same as the percentage of men who
Smoke. Round to the nearest year. What percentage of women and what percentage of men (to the nearest
Whole percent)will smoke at that time?
[Hint: first find the slope-intercept equation of the line that models the percentage, y, of women who
Smoke x years after 1990 and the slope-intercept equation of the line that models the percentage, y, of men
Who smoke x years after 1990]

A)2016; 23%
B)2020; 23%
C)2014; 24%
D)2018; 23%

Question 69

Solve the problem.
You invested $6000 and started a business selling vases. Supplies cost $19 per vase and you are selling each vase for $29. Let x represent the number of vases produced and sold and write the cost function, C,
And revenue function, R. A) $C ( x ) = 19 x + 6000$
$R ( x ) = 29 x$
B) $C ( x ) = 19 x + 29$
$R ( x ) = 6000 x$
C) $C ( x ) = 19 x + 6000$
$\mathrm { R } ( \mathrm { x } ) = 29$
D) $C ( x ) = 19 x + 6000 x$
$R ( x ) = 29 x$

Question 70

Solve the problem.
An-Mei owns a business making and selling jackets. She has a fixed cost of $2100. It costs $97 to produce each jacket. The selling price is $118 per jacket. Determine the number of jackets that must be made and
Sold in order to break even.

A)100 units
B)101 units
C)102 units
D)16 units

Question 71

Solve the problem.
In 1985, in the town of Appleby, 22.8% of Hispanics were overweight, increasing by an average of 0.47% per year. In 1985, in the town of Appleby, 0.17% of whites were overweight, increasing by an average of
29.2% per year. Write a function that models the percentage, y, of Hispanics who are overweight x years
After 1985. Write a function that models the percentage, y, of whites who are overweight x years after 1985. A) Hispanics: $y = 0.47 x + 22.8$
Whites: $\mathrm { y } = 29.2 \mathrm { x } + 0.17$
B) Hispanics: $y = 22.8 x + 0.47$
Whites: $y = 0.17 x + 29.2$
C) Hispanics: $y = 23.27 x$
Whites: $\mathrm { y } = 29.37 \mathrm { x }$
D) Hispanics: $y + 0.47 x = 22.8$
Whites: $\mathrm { y } + 29.2 \mathrm { x } = 0.17$

Question 72

Solve the problem.
A bank teller has 56 $20 and $10 bills in her cash drawer. The value of the bills is $750. How many $20 bills are there?

A)19 $20 bills
B)37 $20 bills
C)21 $20 bills
D)35 $20 bills

Question 73

Solve the problem.
In Miguel's home town, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. The function y = 0.26x + 16.9 models the percentage, y, of women in this city
Who smoke x years after 1990. The function 0.20x + y = 27.3 models the percentage, y, of men in this city
Who smoke x years after 1990. Use these models to determine when the percentage of women who smoke
Will be the same as the percentage of men who smoke. Round to the nearest year. What percentage of
Women and what percentage of men (to the nearest whole percent)will smoke at that time?

A)2013; 23%
B)2014; 23%
C)2012; 23%
D)2015; 22%

Question 74

Solve the problem.
The Family Fine Arts Center charges $22 per adult and $14 per senior citizen for its performances. On a recent weekend evening when 507 people paid admission, the total receipts were $8098. How many who
Paid were senior citizens?

A)382 senior citizens
B)125 senior citizens
C)292 senior citizens
D)215 senior citizens

Question 75

Solve the problem.
A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 4 bags of potato chips for $6.75. Another customer buys 4 hot dogs and 2 bags of potato chips for $6.50. Find the cost of each
Item.

A)$1.25 for a hot dog; $0.75 for a bag of potato chips
B)$0.75 for a hot dog; $1.25 for a bag of potato chips
C)$1.50 for a hot dog; $1.00 for a bag of potato chips
D)$1.25 for a hot dog; $1.00 for a bag of potato chips

Question 76

Solve the problem.
In 1985, in the town of Appleby, 20.4% of Hispanics were overweight, increasing by an average of 0.45% per year. In 1985, in the town of Appleby, 0.18% of whites were overweight, increasing by an average of
30.4% per year. If these trends continue, in which year will the percentage of Hispanics who are
Overweight be the same as the percentage of whites who are overweight? Round to the nearest year. What
Percentage of Hispanics (to the nearest whole percent)will be overweight at that time?

A)1986; 21%
B)1988; 22%
C)1984; 20%
D)1982; 19%

Question 77

Solve the problem.
A rectangular lot whose perimeter is 440 feet is fenced along three sides. An expensive fencing along the lot's length costs $23 per foot , and an inexpensive fencing along the two side widths costs only $11 per
Foot. The total cost of the fencing along the three sides comes to $4960. What are the lot's dimensions?

A)Length 120 ft; Width 100 ft
B)Length 127 ft; Width 93 ft
C)Length 114 ft; Width 106 ft
D)Length 240 ft; Width 200 ft

Question 78

Solve the problem.
Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 2 times as many dimes as nickels, and the value of the dimes is
$0.90 more than the value of the nickels. How many nickels and dimes does Jamil have?

A)6 nickels and 12 dimes
B)7 nickels and 14 dimes
C)5 nickels and 10 dimes
D)12 nickels and 6 dimes

Question 79

Solve the problem.
As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The weekly supply and demand models for a certain type of television are as follows:
Demand: $\mathrm { N } = - 3 \mathrm { p } + 780$
Supply: $\quad N = 2.6 p$
where $p$ is the price in dollars per television.
How many of these televisions can be sold and supplied at $\$ 100$ per television?

A) sold: 480; supplied: 260
B) sold: 1080; supplied: 260
C) sold: 480 ; supplied: 1040
D) sold: 260; supplied: 480

Question 80

Solve the problem.
Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 5 feet more than 6 times the width. He needs 122 feet of fencing to do the job. Find
The length and width of the garden.

A)length: 53 feet; width: 8 feet
B)length: 105 2 feet; width: 165 feet 7 7
C)length: 59 feet; width: 9 feet
D)length: 47 feet; width: 7 feet