### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Find The Sale Price

Mary wants to buy a new skirt. It was originally $30, but is marked 20% off. She also received a coupon for 15% off the sale price. How much will Mary pay for the skirt?

**Possible Answers:**

$19.50

$23.90

$20.40

$10.50

**Correct answer:**

$20.40

20% off means that the new price of the skirt will be 80% of the original price:

$30(100% – 20%) = $30(80%)

Converting the percent to a decimal gives:

$30(0.8) = $24.00

There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:

$24(100% – 15%) = $24(85%)

Again converting the percent to a decimal gives:

$24(0.85) = $20.40

### Example Question #1 : How To Find The Sale Price

A tablet computer listed at an original price of $250 is placed on sale for 20% off the original price. Bob, an employee of the store, gets an additional 30% off the sale price. What price would Bob pay to purchase the tablet computer?

**Possible Answers:**

$125

$100

$140

$200

**Correct answer:**

$140

Take the original price and take off 20% = $250(1 - .2) = $250(.8) = $200

Then take off another 30% $200(1 - .3) = $140

### Example Question #1 : Sale Prices

The manager of a department store decided to raise the price of a certain pair of shoes by 30%. The next day, the store ran a sale of 20% off all items. What is the difference in price, in percentage terms, between the initial price of the shoes and the sale price?

**Possible Answers:**

The price decreased by 10%

The price increased by 10%

The price increased by 4%

The price increased by 1.5%

The price decreased by 4%

**Correct answer:**

The price increased by 4%

To find the price after the initial 30% increase by the manager, you must multiply the original price by 1.3. Then, to find the price after the 20% off sale, you must multiply the new price by 0.8. The original price, therefore, is being multiplied by 1.3*0.8 = 1.04, indicating a 4% overall increase.

### Example Question #4 : How To Find The Sale Price

A shirt is originally priced at $54. It is on sale for 60% off, and Jeff has a coupon for an additional 15% off the reduced price. What is the final price Jeff pays for the shirt?

**Possible Answers:**

$24.30

$4.86

$13.50

$21.60

$18.36

**Correct answer:**

$18.36

After 60% off, the shirt is marked down to $21.60 (found by: $54 - $54*0.6 = $21.60). Jeff uses a 15% off coupon, knocking the price down to $18.36 ( found by: $21.60 - $21.60*0.15 = $18.36).

### Example Question #1 : How To Find The Sale Price

A video game console with a list price of $500 is marked down 20%. If Katie gets an employee discount of 10% off the sale price, how much does she pay for the video game console?

**Possible Answers:**

$350

$340

$400

$360

$450

**Correct answer:**

$360

First find the sale price. Multiply the list price by .2 and subtract that from the list price. 500 – 500 * .2 = 500 – 100 = 400. Now take the employee discount from the new price, 400 – 400 * .1 = 400 – 40 = 360, so Katie would pay $360 for the video game console.

### Example Question #1 : How To Find The Sale Price

A shirt, originally $50, is on sale for 20% off. If Andrew has a coupon that takes 15% off the reduced price, what does he pay?

**Possible Answers:**

$37.00

$34.00

$10.00

$32.50

**Correct answer:**

$34.00

The shirt is on sale for 50 x .8 = $40. If Andrew takes another 15% off, he will pay $40 x .85= $34.00

### Example Question #7 : How To Find The Sale Price

A blue dress is marked down 15%. What is the sale price of the dress if the regular price is $150?

**Possible Answers:**

$137.50

$127.50

$115.25

$140.00

$103.50

**Correct answer:**

$127.50

There are two ways to work this problem.

The first way is to find the amount of the discount and subtract from the original price: 0.75 * 150 = 22.50, then 150 – 22.50 = 127.50

The second method finds the sales price directly: 100% = % Discount + % Sales Price or 1 – % Discount = % Sales Price

1 – 0.15 = 0.85, so the sales price is 0.85 * 150 = 127.50

### Example Question #1 : How To Find The Sale Price

Gina wants to purchase a new television. It was originally $500, but is marked 25% off. She also received a coupon for 10% off the sale price. How much will Gina pay for the television?

**Possible Answers:**

$465

$102.50

$375.25

$350.00

$337.50

**Correct answer:**

$337.50

25% off means that the new price of the television will be 75% of the original price:

$500(100% – 25%) = $500(75%)

Converting the percent to a decimal gives:

$500(0.75) = $375.00

There is an additional 10% off the sale price of $375.00, so the final price is 90% of the sale price:

$24(100% – 10%) = $375(90%)

Again converting the percent to a decimal gives:

$375(0.9) = $337.50

So, we choose C.

### Example Question #2 : How To Find The Sale Price

The grocery store is having a sale on cereal. The sale is 20% off each box if you buy 3 boxes of the same type and 40% off each box if you buy 5 boxes of the same type. You purchase one box of puffed rice priced at $3.50, three boxes of bran flakes priced at $4.25 and five boxes of granola priced at $5.00. What is the total price after the discount is applied.

**Possible Answers:**

$10.00

$28.70

$25.00

$28.50

$15.00

**Correct answer:**

$28.70

Puffed rice: 1 box at full price = $3.50

Bran Flakes: 3 boxes at 20% off of $4.25 = (3 * 4.25) * 0.20 = (12.75) * 0.20 = $2.55

Cost = $12.75 – $2.55 = $10.20

Granola: 5 at 40% off of $5.00 = (5 * 5.00) * 0.40 = (25) * 0.40 = $10.00

Cost = $25.00 – $10.00 = $15.00

Total Cost = $3.50 + $10.20 + $15.00 = $28.70

### Example Question #1 : How To Find The Sale Price

An ecomony car gets 34 miles per gallon. If gas is currently priced at $3.98 per gallon, how much would the gas cost for this car to travel 400 miles.

**Possible Answers:**

$82.46

$43.32

$64.28

$26.48

$46.82

**Correct answer:**

$46.82

The car needs to travel 400 miles so divide 400 by 34 to find the number of gallons required. Then multiply by the price per gallon to find the amount required.

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