Percentage

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ACT Math › Percentage

Questions 1 - 10

If $\dpi{100} \small 80%$ of a number is $\dpi{100} \small 240$ , what is $\dpi{100} \small 125%$ of the number?

$\dpi{100} \small 375$

$\dpi{100} \small 300$

$\dpi{100} \small 325$

$\dpi{100} \small 200$

$\dpi{100} \small 250$

Explanation

Since $\dpi{100} \small 80%$ of the number is $\dpi{100} \small 240$ , the number is $\dpi{100} \small \frac{240}{.80}$ which equals $\dpi{100} \small 300$ . Then calculate $\dpi{100} \small 125%$ of $\dpi{100} \small 300$ :

$\dpi{100} \small 1.25\times 300=375$ .

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?

$128

$160

$208

$240

$272

Explanation

First find the original price of the couch. If $320 represents the price after taking 20% off, then $320 = 80% of the original price. To find the original price, divide (320) / (0.8) = 400.

Then find the "additional sale" price. The couch has been marked down an additional 40% from the sale price of $320. Since "40% off" means that you pay 60% of what you would have, multiply the sale price of $320 by the 60% that Max pays. $320 * 0.6 = $192.

Finally, do the subtraction of the original price minus the price Max paid: $400 – $192 = $208.

76 eleventh-grade students turned in term papers on the United States Constitution. 3 students failed, 26 students recieved C's, 31 students recieved B's. The remaining students earned A's on their papers.

What percentage of students earned A's on their paper? (Round to the nearest percent.)

$\dpi{100} \small 21%$

$\dpi{100} \small 16%$

$\dpi{100} \small 50%$

$\dpi{100} \small 25%$

$\dpi{100} \small 10%$

Explanation

Subtract 3, 26, and 31 from 76 to figure out how many students got A's (16).

$\dpi{100} \small \frac{16}{76} \times 100$

A bowl contains marbles that are either red or green. The probability of selecting a red marble at random from the bowl is

Which of the following expressions represents the total number of red marbles in the bowl?

$\frac{x}{25}$

$\frac{25x}{10}$

$\frac{2.5x}{10}$

Explanation

It’s best to start with a fraction that is a part over 100. For this problem, we are looking for a fraction that shows $\frac{25}{100}$ . If you go through the choices available, $\frac{2.5}{10}=\frac{25}{100}$ . Therefore, if you plug in any value for “X” in this fraction, you will know the total number of marbles in the bowl. Here is an example:

If there are 4 marbles in the bowl, you’d expect 1 to be red. If we use this equation, we get

$\frac{(2.5)(4)}{10}=\frac{10}{10}=1$

What percentage of students earned A's on their paper? (Round to the nearest percent.)

$\dpi{100} \small 21%$

$\dpi{100} \small 16%$

$\dpi{100} \small 50%$

$\dpi{100} \small 25%$

$\dpi{100} \small 10%$

Explanation

Subtract 3, 26, and 31 from 76 to figure out how many students got A's (16).

$\dpi{100} \small \frac{16}{76} \times 100$

Which of the following fractions is equivalent to

$4 \frac{31}{50}$

$3 \frac{18}{25}$

$5 \frac{2}{5}$

$3 \frac{4}{5}$

$4 \frac{18}{25}$

Explanation

To convert an integer percentage into an improper fraction, set the percentage as a fraction over and simplify as far as you can. At that point, simply convert the improper fraction into a mixed fraction.

$462 % = \frac{462}{100} = \frac{231}{50} = 4 \frac{31}{50}$

What percentage of students earned A's on their paper? (Round to the nearest percent.)

$\dpi{100} \small 21%$

$\dpi{100} \small 16%$

$\dpi{100} \small 50%$

$\dpi{100} \small 25%$

$\dpi{100} \small 10%$

Explanation

Subtract 3, 26, and 31 from 76 to figure out how many students got A's (16).

$\dpi{100} \small \frac{16}{76} \times 100$

A dress is priced at $375 and a pair of shoes are $150. If they are both on sale for 30% off, what is price of purchasing them both on sale?

$367.50

$157.50

$525.50

$281.50

$393.75

Explanation

$375 + $150 = $525

Sale price is 30% off or (0.3)($525) = $157.50

Subtract the discount from the initial price: $525 – $157.50 = $367.50

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?

$\dpi{100} \small \$ 16.80$

$\dpi{100} \small \$ 18.00$

$\dpi{100} \small \$ 21.00$

$\dpi{100} \small \$ 12.00$

$\dpi{100} \small \$ 17.50$

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.

$128

$160

$208

$240

$272

Explanation

First find the original price of the couch. If $320 represents the price after taking 20% off, then $320 = 80% of the original price. To find the original price, divide (320) / (0.8) = 400.

Finally, do the subtraction of the original price minus the price Max paid: $400 – $192 = $208.

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