### All ACT Math Resources

## Example Questions

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

Max wants to buy a couch at The Furniture Store. The couch he is considering had been marked on sale for 20% off and was selling for $320. The day he comes in to buy the couch, it has been marked down an additional 40% off of the sale price. What is the difference in the original price of the couch and what Max paid for the couch?

**Possible Answers:**

$160

$272

$240

$128

$208

**Correct answer:**

$208

(320) / (0.8) = 400. The couch has been marked down an additional 40% from the sale price of $320. $320 * 0.6 = $192. $400 – $192 = $208.

### 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

$20.40

$10.50

$23.90

**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 #2 : 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:**

$200

$125

$140

$100

**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 #3 : How To Find The Sale Price

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 increased by 10%

The price increased by 4%

The price decreased by 4%

The price increased by 1.5%

The price decreased by 10%

**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 #2 : 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:**

$21.60

$4.86

$18.36

$24.30

$13.50

**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 #6 : 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:**

$360

$400

$350

$450

$340

**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 #2 : 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:**

$34.00

$37.00

$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 #2 : 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:**

$103.50

$140.00

$115.25

$127.50

$137.50

**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 #3 : Sale Prices

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:**

$350.00

$465

$102.50

$337.50

$375.25

**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 #3 : Sale Prices

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:**

$28.50

$25.00

$10.00

$28.70

$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