Question 1

Solve.
-You are traveling to your aunt's house that is 192 miles away. If you are currently twice as far from home as you are from your aunt's, how far have you traveled?

Accepted Answer

You have traveled 128 miles. If you are twice as far from home as from your aunt's, the distance you are from home is 192 - x, and the distance from your aunt's is x. Setting up the equation 2x = 192 - x and solving for x gives x = 128 miles.

Question 2

Solve.
-Alex sold his used electric saw and accessories for $336. If he received five times as much money for the electric saw as he did for the accessories, how much did he receive for the electric saw?

Accepted Answer

Let the amount received for the accessories be x dollars. Therefore, the amount received for the electric saw is 5x dollars. According to the problem, x + 5x = 336. Solving this equation, we get 6x = 336, which means x = 56. Therefore, the amount received for the electric saw is 5x = 5 * 56 = $280.

Question 3

Solve the problem.
-Every basketball season Pam competes in a free throw contest. This year Pam was successful at 0.75 of her free throws. If she succeeded at 9 free throws, how many free throws did she attempt?

Accepted Answer

Pam's success rate is 0.75, and she succeeded at 9 free throws. To find the total attempts, divide the number of successful free throws by the success rate: 9 / 0.75 = 12.

Question 4

Solve the problem.
-A pie-shaped (triangular) lake-front lot has a perimeter of 2000 feet. One side is 300 feet longer than the shortest side, while the third side is 500 feet longer than the shortest side. Find the lengths of all three sides.

Accepted Answer

Let the shortest side be x feet. Then, the other sides are x + 300 feet and x + 500 feet. The perimeter is the sum of all sides, so x + (x + 300) + (x + 500) = 2000. Simplifying, 3x + 800 = 2000, leading to 3x = 1200, and x = 400 feet. Thus, the sides are 400 ft, 700 ft (400 + 300), and 900 ft (400 + 500).

Question 5

Solve.
-A car rental business rents a compact car at a daily rate of $28.20 plus 20¢ per mile. Mike can afford to spend $73 on the car rental for one day. How many miles can he drive and stay within his budget? (Hint: 20¢ = $0.20)

Accepted Answer

The correct answer is A.The total cost of the car rental is $28.20 plus 20¢ per mile. We can write this as an equation:Total cost = $28.20 + $0.20 per mileWe know that Mike can afford to spend $73 on the car rental, so we can set the total cost equal to $73 and solve for the number of miles:$73 = $28.20 + $0.20 per mile$44.80 = $0.20 per mile224 miles = $0.20 per mileTherefore, Mike can drive 224 miles and stay within his budget.

Question 6

Solve.
-A city government budgeted $28.2 million for public transportation. This was $14.4 million more than was budgeted for parks and recreation. How much was budgeted for parks and recreation?

Accepted Answer

To find the budget for parks and recreation, subtract the additional amount for public transportation from the total budgeted for it: $28.2 million - $14.4 million = $13.8 million.

Question 7

Solve.
-A 369-foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is 3 times as long as the second. How long is each piece of rope?

Accepted Answer

The answer of Solve.
-A 369-foot rope is cut into three...

Question 8

Solve the problem.
-On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 6%. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $1378? Round to the
Nearest dollar if necessary.

Accepted Answer

The answer of Solve the problem.
-On Monday, an investor bought...

Question 9

Solve.
-The area of Mark's backyard is about 5 times the area of Jon's backyard. The area of Mark's backyard is  . What is the area of Jon's backyard?

Accepted Answer

The answer of Solve.
-The area of Mark's backyard is about...

Question 10

Solve the problem.
-If Gloria received a 3 percent raise and is now making $21,630 a year, what was her salary before the raise? Round to the nearest dollar if necessary.

Accepted Answer

Gloria's new salary is the result of a 3% raise, so her previous salary was 100% of her original salary. To find the original salary, divide her new salary by 1.03 (100% + 3% = 103%, or 1.03 as a decimal). $21,630 / 1.03 = $21,000 (rounded to the nearest dollar).

Question 11

Solve the problem.
-At the end of the day, a storekeeper had $1712 in the cash register, counting both the sale of goods and the sales tax of 7%. Find the amount that is the tax. Round to the nearest dollar if necessary.

Accepted Answer

The answer of Solve the problem.
-At the end of the...

Question 12

Solve.
-The height of the tallest building in Anne's home town is 735 feet, which is about 390 feet taller than the tallest building in Laurie's home town. What is the height of the tallest building in Laurie's home town?

Accepted Answer

The height of the tallest building in Laurie's home town is 735 feet - 390 feet = 345 feet.

Question 13

Solve the problem.
-Brand X copier advertises that its copiers run 12% longer between service calls than its competitor. If Brand X copiers run 52,600 copies between service calls, how many copies would the competitor run (to the nearest
Copy)?

Accepted Answer

Brand X runs 12% longer than its competitor, meaning Brand X's performance is 112% of its competitor's. To find the competitor's performance, divide Brand X's performance by 1.12: 52,600 / 1.12 = 46,964 copies (rounded to the nearest copy).

Question 14

Solve.
-Elaine was cooking dinner for some friends. She went out to do the shopping and spent $120. She spent twice as much on food as on drinks. How much did she spend on each?

Accepted Answer

The answer of Solve.
-Elaine was cooking dinner for some friends....

Question 15

Solve the problem.
-Stevie bought a stereo for $260 and put it on sale at his store at a 60% markup rate. What was the retail price of the stereo? Round to the nearest cent if necessary.

Accepted Answer

The retail price is calculated by adding the markup to the original price. A 60% markup on $260 is $260 * 0.60 = $156. Adding this to the original price, $260 + $156 = $416.

Question 16

Solve the problem.
-A baseball team played 171 complete games last season. They had 7 fewer wins than losses. How many games did the team win?

Accepted Answer

Let the number of wins be W and the number of losses be L. We know that W + L = 171 and W = L - 7. Solving these equations simultaneously, we find that the team won 82 games.

Question 17

Solve the problem.
-CopyMart charges $27 plus 45¢ per copy to produce promotional brochures. How many brochures can Steve purchase if he has a budget of $77.85? (Hint: 45¢ = $0.45)

Accepted Answer

To find the number of brochures Steve can purchase, set up the equation: $27 + $0.45x = $77.85, where x is the number of brochures. Solving for x gives x = (77.85 - 27) / 0.45 = 113 brochures.

Question 18

Solve the problem.
-A high school graduating class is made up of 499 students. There are 147 more girls than boys. How many boys are in the class?

Accepted Answer

Let the number of boys be x. Then, the number of girls is x + 147. The total number of students is the sum of boys and girls, which is x + (x + 147) = 499. Solving for x gives 2x + 147 = 499, 2x = 352, and x = 176.

Question 19

Solve the problem.
-On a road trip from New York to Los Angeles, Peter stopped in St. Louis which is 924 miles from New York. If St. Louis is 0.33 of the trip to Los Angeles, how far is it from New York to Los Angeles?

Accepted Answer

Since St. Louis is 0.33 (or 1/3) of the trip to Los Angeles, the total distance from New York to Los Angeles is 924 miles / 0.33 = 2800 miles.

Question 20

Solve the problem.
-Recently, the cost of 14 6-oz jars of baby food was $9.24. What was the cost of one jar?

Accepted Answer

To find the cost of one jar, divide the total cost by the number of jars: $9.24 ÷ 14 = $0.66.

Quiz 3: Solving Equations and Inequalities

Solve. -You are traveling to your aunt's house that is 192 miles away. If you are currently twice as far from home as you are from your aunt's, how far have you traveled?

Solve. -Alex sold his used electric saw and accessories for $336. If he received five times as much money for the electric saw as he did for the accessories, how much did he receive for the electric saw?

Solve the problem. -Every basketball season Pam competes in a free throw contest. This year Pam was successful at 0.75 of her free throws. If she succeeded at 9 free throws, how many free throws did she attempt?

Solve the problem. -A pie-shaped (triangular) lake-front lot has a perimeter of 2000 feet. One side is 300 feet longer than the shortest side, while the third side is 500 feet longer than the shortest side. Find the lengths of all three sides.

Solve. -A car rental business rents a compact car at a daily rate of $28.20 plus 20¢ per mile. Mike can afford to spend $73 on the car rental for one day. How many miles can he drive and stay within his budget? (Hint: 20¢ = $0.20)

Solve. -A city government budgeted $28.2 million for public transportation. This was $14.4 million more than was budgeted for parks and recreation. How much was budgeted for parks and recreation?

Solve. -A 369-foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is 3 times as long as the second. How long is each piece of rope?

Solve the problem. -On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 6%. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $1378? Round to the Nearest dollar if necessary.

Solve. -The area of Mark's backyard is about 5 times the area of Jon's backyard. The area of Mark's backyard is . What is the area of Jon's backyard?

Solve the problem. -If Gloria received a 3 percent raise and is now making $21,630 a year, what was her salary before the raise? Round to the nearest dollar if necessary.

Solve the problem. -At the end of the day, a storekeeper had $1712 in the cash register, counting both the sale of goods and the sales tax of 7%. Find the amount that is the tax. Round to the nearest dollar if necessary.

Solve. -The height of the tallest building in Anne's home town is 735 feet, which is about 390 feet taller than the tallest building in Laurie's home town. What is the height of the tallest building in Laurie's home town?

Solve the problem. -Brand X copier advertises that its copiers run 12% longer between service calls than its competitor. If Brand X copiers run 52,600 copies between service calls, how many copies would the competitor run (to the nearest Copy) ?

Solve. -Elaine was cooking dinner for some friends. She went out to do the shopping and spent $120. She spent twice as much on food as on drinks. How much did she spend on each?

Solve the problem. -Stevie bought a stereo for $260 and put it on sale at his store at a 60% markup rate. What was the retail price of the stereo? Round to the nearest cent if necessary.

Solve the problem. -A baseball team played 171 complete games last season. They had 7 fewer wins than losses. How many games did the team win?

Solve the problem. -CopyMart charges $27 plus 45¢ per copy to produce promotional brochures. How many brochures can Steve purchase if he has a budget of $77.85? (Hint: 45¢ = $0.45)

Solve the problem. -A high school graduating class is made up of 499 students. There are 147 more girls than boys. How many boys are in the class?

Solve the problem. -On a road trip from New York to Los Angeles, Peter stopped in St. Louis which is 924 miles from New York. If St. Louis is 0.33 of the trip to Los Angeles, how far is it from New York to Los Angeles?

Solve the problem. -Recently, the cost of 14 6-oz jars of baby food was $9.24. What was the cost of one jar?