### All ACT Math Resources

## Example Questions

### Example Question #1301 : Act Math

Patrice earns $75 per day. Ron earns $350 per week. How many days does Patrice have to work to earn more than what Ron earns in 5 weeks?

**Possible Answers:**

20

25

23

24

**Correct answer:**

24

Find out how much Ron earns in 5 weeks ($1750). Divide by Patrice’s daily wage (23.3333 days). Patrice needs to work at least 24 days. At 23 days, she will only have earned $1725, falling $25 short of Ron’s 5 week earnings.

### Example Question #1 : How To Find Amount Of Profit

A business launches a new product that produces $x in sales its first year. Sales in the second year are double the first, and the third year has sales four times as large as the first year. If 2^{nd} year sales were $12 million, how much in total sales was produced over the 3 year period?

**Possible Answers:**

$40 million

$36 million

$42 million

$48 million

**Correct answer:**

$42 million

Write out an equation. Total sales = T = x +2x + 4x

If 2x = 12, x = 6

T = 6 + 12 + 24 = $42 million

### Example Question #2 : How To Find Amount Of Profit

A jewelry designer bought a booth at a local craft fair. She paid $160 for the booth rental for the day. Her necklaces cost $10 to make and she sells them for $50 apiece. If she wants to make at least $1000 profit for the day, how many necklaces must she sell?

**Possible Answers:**

29

18

24

22

20

**Correct answer:**

29

Profit on Necklace = Price – Cost = $50 – $10 = $40

Total Profit = # of Necklaces Sold * $40 – Booth Rental Rate

$1000 Profit = # of Necklaces * $40 – $160

$1160 = # of Necklaces * $40

# Necklaces = 29

### Example Question #1 : Profit Margin

A law firm earned $2,000,000 this year in fees. If the firm’s annual operating costs are $1,250,000, what is their profit this year?

**Possible Answers:**

$2,000,000

$250,000

$1,250,000

$1,000,000

$750,000

**Correct answer:**

$750,000

Profit = Total Fees – Operating Costs = $2,000,000 – $1,250,000 = $750,000

### Example Question #151 : Percentage

Max bought a book for $10. If he later sold the book at a 25% profit. How much money in total did he receive from the sale of the book?

**Possible Answers:**

$7.50

$10

$15

$12.50

**Correct answer:**

$12.50

If the book is sold at a profit we know that the sale price is more than what he bought it for. 25% of $10 is $2.50. Therefore the sale price is $10 + $2.50 which is $12.50. It could also be seen as $10 X 1.25 =$12.50

### Example Question #3 : Profit Margin

Sam was helping his school raise funds to buy books for the library. He bought small paper pads for $0.75 and sold them for $2.00. What was the percent mark-up, rounded to the nearest whole number?

**Possible Answers:**

66%

None of the answers are correct

75%

167%

150%

**Correct answer:**

167%

$ Mark-Up = $ New Price – $ Original Price

% Mark-Up = $ Mark-Up ÷ $ Original Price

% Mark-Up = (2.00 – 0.75) ÷ 0.75 = 1.67 or 167 %

### Example Question #4 : Profit Margin

Jenny has two jobs. The first is an office job salaried at $52,000 per year, so she makes the same amount of money every week, no matter how many hours she works. The second is a bartending job. She works 6 hours a night, 2 nights a week. She earns $3.50 per hour plus tips. If she earned $450 in tips this week, what is the total amount of money she made this week?

**Possible Answers:**

$1,021

$1,450

$1,000

$1,480

$1,492

**Correct answer:**

$1,492

Salaried job:

$52,000 / year

1 year = 52 weeks

Therefore: $52,000 / 52 weeks = $1,000.00 per week

Bartending job:

6 hours x $3.50 per hour x 2 nights per week = $42.00

Total Earned = Salaried + Bartending + Tips

= $1,000.00 + $42.00 + $450 = $1,492

### Example Question #1 : How To Find Amount Of Profit

A chair company produces 5,000 luxury chairs per year. Each chair requires $200 in wood and other materials to build. It also requires 3 hours of work by a craftsman, who earns $30 per hour. If the company wants to earn $3 million dollars in profit this year, how much should each chair cost?

**Possible Answers:**

$850

$800

$750

$890

$900

**Correct answer:**

$890

Total cost of chair = materials + labor = $200 + (3 hours) ($30/hour) = $290

Total cost for 5000 chairs = $290 x 5,000 = $1,450,000

Profit = (5000) x Price per chair – Cost of Chairs

$3,000,000 = (5000) x Price per chair – $1,450,000

$4,450,000 = (5000) x Price per chair

Price per chair = $4,450,000 / 5,000 = $890

### Example Question #6 : Profit Margin

A company made in sales last year. The company has four employees. Two of the employees earn per year, and the other two employees earn per year.

In addition to employee salaries, the company also pays a month in rent for its office space and per month in general expenses.

What was the company's profit last year?

**Possible Answers:**

**Correct answer:**

Annual profit = Total Annual Sales – Total Annual Expenses

Total Annual Sales = $400,000

Total Annual Expenses = Salaries + Rent + Expenses

2 employees @ $50,000 = $100,000

2 employees @ $70,000 = $140,000

12 months of rent @ $5,000 = $60,000

12 months of expenses @ $4,000 = $48,000

Total Annual Expenses = $348,000

Annual profit = $400,000– $348,000 = $52,000

### Example Question #2 : Profit Margin

Madame buys 5 dozen eggs at 10 cents per egg. She then sells each dozen for 2 dollars. What is her profit margin?

**Possible Answers:**

**Correct answer:**

Profit margin is equal to profit / revenue. She bought the eggs for (5)(12)(0.1) = $6 total. She is selling the eggs for (5)(2)=$10 total.

The profit margin is equal to or

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