Question 1

Solve

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...

Question 2

Solve using any method.

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 ...

Question 3

Solve using any method. Round to two decimal places if necessary.

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Question 4

Juan uses a 10% off total purchase coupon at his local supermarket. His checkout price before tax is $103.75. How much would he have paid without the coupon?

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Question 5

Lucas, Rebecca, and Brandon order a large pizza. They decide to split the cost according to how much they will eat. Brandon pays $2.32, Rebecca eats 1/6 of the pizza, and Lucas eats 4/7 of the pizza. How much did the pizza cost?

Accepted Answer

To find the total cost of the pizza, we need to determine how much each person paid based on their share. Brandon's payment of $2.32 represents his share of the pizza. Rebecca eats 1/6 and Lucas eats 4/7, so the remaining portion for Brandon is 1 - (1/6 + 4/7) = 1/42. Since Brandon's payment of $2.32 corresponds to 1/42 of the pizza, the total cost is $2.32 * 42 = $8.86.

Question 6

A college bookstore marks up the price it pays the publisher for a book by 25%. If the selling price of a book is $82, how much did the bookstore pay for the book?

Accepted Answer

The bookstore's selling price is 125% of the price it paid. So, $82 is 125% of the cost price. To find the cost price, divide $82 by 1.25, which equals $65.60.

Question 7

A builder of tract homes reduced the price of a model by 15%. If the new price is $167,170, what was its original price?

Accepted Answer

To find the original price, divide the new price by (1 - 0.15), which is 0.85. So, $167,170 / 0.85 = $196,670.59.

Question 8

A company has a total of $11,750 allocated for monthly costs. Fixed costs are $6650 a month and variable costs are $13 per unit. How many units can be manufactured a month?

Accepted Answer

To find the number of units that can be manufactured, subtract the fixed costs from the total budget to find the amount available for variable costs: $11,750 - $6,650 = $5,100. Then, divide this amount by the variable cost per unit: $5,100 / $13 = 392 units.

Question 9

Lacie decides to start a small business making monogrammed towels. She can set aside $4670 for monthly costs. Fixed costs are $1800 per month and variable costs are $4 per set of towels. How many sets of towels can she afford to make per month?

Accepted Answer

To find the number of sets of towels she can afford to make, subtract the fixed costs from the total monthly budget and then divide by the variable cost per set: (4670 - 1800) / 4 = 717 sets.

Question 10

Find the perimeter of a triangle if one side is 35 feet, another side is 1/4 of the perimeter, and the third side is 1/3 of the perimeter. Round your answer to 2 decimal places.

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Question 11

The length of a rectangle is 9 more feet than 4 times its width. The perimeter of the rectangle is 358 feet. What is the length of the rectangle?

Accepted Answer

The length of the rectangle is 9 more feet than 4 times its width, so the length is 4w + 9. The perimeter of the rectangle is 2(length + width), so 2(4w + 9 + w) = 358. Solving for w gives w = 20. Therefore, the length of the rectangle is 4w + 9 = 4(20) + 9 = 145 feet.

Question 12

William has $14,550 to invest and decides to put some in a CD that earns 2.25% interest per year and the rest in a low risk stock that earns 3.4%. How much did he invest to earn $395.225 interest in the first year?

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Question 13

BJ bought ham and cheese at the deli. The ham costs $6.50 per pound and the cheese costs $4.90 per pound. In total, BJ bought 7.6 pounds and the price was $40.6. How many pounds of each did BJ buy?

Accepted Answer

Let x be the number of pounds of ham and y be the number of pounds of cheese.We have the following system of equations:x + y = 7.66.50x + 4.90y = 40.6Solving this system of equations, we get:x = 2.10y = 5.5Therefore, BJ bought 2.10 pounds of ham and 5.5 pounds of cheese.

Question 14

A motorboat can maintain a constant speed of 12 miles per hour relative to the water. The boat makes a trip upstream in 42 minutes and the return trip takes 21 minutes. What is the speed of the current?

Accepted Answer

The speed of the boat relative to the water is 12 mph. Let the speed of the current be x mph. Upstream, the effective speed is (12 - x) mph, and downstream, it is (12 + x) mph. The time taken upstream is 42 minutes (0.7 hours) and downstream is 21 minutes (0.35 hours). Using the formula distance = speed × time, the distances for both trips are equal: (12 - x) * 0.7 = (12 + x) * 0.35. Solving this equation gives x = 4 mph.

Question 15

Lee can mow a lawn in 10 minutes. It takes Ito 60 minutes to mow a lawn of the same size. How long would it take them to mow the lawn if they work together?

Accepted Answer

Lee's rate is 1 lawn per 10 minutes, and Ito's rate is 1 lawn per 60 minutes. Together, their combined rate is 1/10 + 1/60 = 1/8.57 lawns per minute. Therefore, it would take them approximately 8.6 minutes to mow the lawn together.

Question 16

Aleshia's test scores are 76, 83, 95, and 89. The final will count as two tests. What score does Aleshia need on the final to have an average score of 80?

Accepted Answer

To find the score needed on the final, set up the equation: (76 + 83 + 95 + 89 + 2x) / 6 = 80. Solving for x gives x = 68.5.

Question 17

A college bookstore marks up the price it pays the publisher for a book by 23%. If the selling price of the book is $107.01, how much did the bookstore pay for the book?

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Question 18

The length of a rectangle is 4 feet more than 4 times its width. The perimeter of the rectangle is 148 feet. What is the length of the rectangle?

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Question 19

The Parsons budgeted $147.00 to landscape their yard with trees and shrubs. Trees each cost $16.50 and shrubs each cost $9.50. Combined they planted a total of 14 trees and shrubs. How many of each did they plant in their yard?

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Question 20

For a certain experiment, a student requires 20 mL of a solution that is 11% HCl (hydrochloric acid). The store-room has only solutions that are 8% HCl and 12% HCl. How many milliliters of each available solution should be mixed to get 20 mL of 11% HCl?

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Quiz 1: Equations and Inequalities