ACT Math : Percentage

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : 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:

$18.36

$24.30

$13.50

$4.86

$21.60

Correct answer:

$18.36

Explanation:

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:

$340

$350

$450

$360

$400

Correct answer:

$360

Explanation:

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:

$32.50

$34.00

$10.00

$37.00

Correct answer:

$34.00

Explanation:

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 #1 : 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:

$140.00

$103.50

$137.50

$127.50

$115.25

Correct answer:

$127.50

Explanation:

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:

$337.50

$465

$375.25

$102.50

$350.00

Correct answer:

$337.50

Explanation:

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 #1 : 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:

$15.00

$28.50

$25.00

$28.70

$10.00

Correct answer:

$28.70

Explanation:

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 #111 : Percentage

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:

$46.82

$43.32

$64.28

$26.48

$82.46

Correct answer:

$46.82

Explanation:

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.

Example Question #111 : Percentage

A store buys a new line of dresses for $15.00 each. They increase this price by 40% when they sell the dresses in the store. This week, the dresses are on sale for 20% off. What is the price of one dress this week?

Possible Answers:

\dpi{100} \small \$ 21.00

\dpi{100} \small \$ 12.00

\dpi{100} \small \$ 16.80

\dpi{100} \small \$ 17.50

\dpi{100} \small \$ 18.00

Correct answer:

\dpi{100} \small \$ 16.80

Explanation:

The price of one dress is now $16.80. The original price was $15.00. When the dresses were sold in the store, the price was increased by 40%, to $21.00 

(15+15\times 0.4=21)

Then, the price was decreased by 20%, to $16.80.

(21-21\times 0.2=16.8)

It might be tempting to just increase the original price by 20%, but the percent increase and the percent decrease must be performed together.

Example Question #11 : How To Find The Sale Price

Carl's new bike cost a total of \$146.28 after a state sales tax of 6\% was applied. What was the original price of Carls bike before the sales tax was applied? 

Possible Answers:

\$138

\$134

\$130

\$136

\$132

Correct answer:

\$138

Explanation:

Create an equation which will help you find the missing price (x).

The missing price, plus 6\% of the missing price equals \$146.28

x+(.06x)=146.28

1.06x=146.28

x=138

Example Question #13 : How To Find The Sale Price

Jacob bought a leather wallet for a final price of $32.73. It had been marked down by 15%. Jacob had also used a 10% off coupon, calculated after the 15% off. What was the original price of the wallet?

Possible Answers:

\$40.90

\$42.78

\$43.64

\$38.51

\$36.37

Correct answer:

\$42.78

Explanation:

Taking 10% off the price is the same as paying 90% of the price; just as taking 15% off the price is the same as paying 85% of the price. Taking 85% of the original price and then 90% of the new price is quickly found by multiplying .90 and .85 together. Using algebra:

\small (0.90)(0.85)x = \$ 32.73

\small x=\$ 42.78

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