ACT Math : Percentage

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Other Percentage

A high school student spends a total of 90 minutes per day studying for the ACT, Monday through Friday, then 2 hours a day on the weekend.  What percent of their week is spent studying for the ACT? 

Possible Answers:

6.25%

6.8%

7.125%

5.5%

8%

Correct answer:

6.8%

Explanation:

The number of minutes in a week is:

\displaystyle 24\ hrs./day \times 60\ min./hr. \times 7\ days/week = 10,080 \ min./week

The number of minutes spent studying is:

\displaystyle (90\ min./day \times 5) + (120\ min./day \times 2) = 690

\displaystyle 690/10080 = .68 \times 100 = 6.8

6.8%

Example Question #11 : Other Percentage

Student_activities

Above is a chart showing the students and the different activities they are involved in. What percentage of the students are on the soccer team? Round to the nearest tenth of a percent.

Possible Answers:

30.0%

32.5%

37.5%

25.0%

40.0%

Correct answer:

37.5%

Explanation:

Percentage = Students on Soccer Team / Total Number of Students

= 3/8 = .375 = 37.5%

Example Question #12 : Other Percentage

Student_activities

What percentage of the students are involved in both newspaper and soccer?

Possible Answers:

15%

20%

30%

25%

35%

Correct answer:

25%

Explanation:

There are three students involved in soccer.  Read across the chart and two of them are also involved in newspaper.

Percentage = 2/Total Number of Students

= 2/8 = .25 = 25%

Example Question #13 : Other Percentage

The average person spends 30% of their life sleeping.  Assuming the average person lives till the age of 93, how many years will they have spent asleep? Round to the nearest whole number

Possible Answers:

30 years

19 years

9 years

28 years

31 years

Correct answer:

28 years

Explanation:

This problem requires simple arithmetic, 30% of 93 can be obtained by multiply 93 X .30 = 27.9 Rounding yields 28 years.

Example Question #14 : How To Find Percentage

What is 9% of 8,100?

Possible Answers:

729

900

836

459

2,700

Correct answer:

729

Explanation:

8,100 * 0.09 = 729

Example Question #71 : Percentage

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.)

Possible Answers:

\dpi{100} \small 25\%

\dpi{100} \small 10\%

\dpi{100} \small 50\%

\dpi{100} \small 16\%

\dpi{100} \small 21\%

Correct answer:

\dpi{100} \small 21\%

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

Example Question #165 : Arithmetic

What is \displaystyle 73\% of \displaystyle 225?

Possible Answers:

\displaystyle 60.75

\displaystyle 175

\displaystyle 200

\displaystyle 164.25

\displaystyle 180.5

Correct answer:

\displaystyle 164.25

Explanation:

To find the percentage of a number, convert the percentage into a decimal by diving the percent by 100.

\displaystyle \frac{73}{100} = 0.73,

then multiply that decimal by the number. 

\displaystyle 225\cdot 0.73 = 164.25

Example Question #1238 : Act Math

\displaystyle \small 15 is what percent of \displaystyle \small 48? Round to the nearest hundredth.

Possible Answers:

\displaystyle \small 31.25\%

\displaystyle \small 68.75\%

\displaystyle \small 22.95\%

\displaystyle \small 3.2\%

\displaystyle \small 27.5\%

Correct answer:

\displaystyle \small 31.25\%

Explanation:

For percentage problems, the easiest way to start is by remembering that the word "of" is best translated as a multiplication, while the word "is" is best translated by an equals sign. Thus, for the information provided, we can write the equation:

\displaystyle \small 15 = x * 48

Remember, though, that \displaystyle \small x will represent a percentage in a decimal form and will need to be translated. (There are other ways of doing this, but most students remember to do this translation at the end naturally.)

Solving for \displaystyle x, you get:

\displaystyle \small x=\frac{15}{48}=0.3125

This is \displaystyle \small 31.25\%.

Example Question #15 : Other Percentage

What is \displaystyle \small 30\% of \displaystyle \small 52\% of \displaystyle \small 1837?

Possible Answers:

\displaystyle \small 286.572

\displaystyle \small 955.24

\displaystyle \small 617.232

\displaystyle \small 183.14

\displaystyle \small 1506.34

Correct answer:

\displaystyle \small 286.572

Explanation:

For percentage problems, the easiest way to start is by remembering that the word "of" is best translated as a multiplication, while the word "is" is best translated by an equals sign. Thus, for the information provided, we can write the equation:

\displaystyle \small x = 0.3 * 0.52*1837

Solving for \displaystyle x, you get:

\displaystyle \small \small x = 286.572

Alternatively you could first calculate \displaystyle 52\% of \displaystyle 1837, which is \displaystyle 955.24, and then calculate \displaystyle 30\% of that, and you would arrive at the same answer.

Example Question #171 : Arithmetic

A computer originally sold for \displaystyle \$1837 dollars. Its price was reduced by \displaystyle \small 30\% and then again by \displaystyle \small 25\%. What was the final sale price for the computer? Round to the nearest cent.

Possible Answers:

\displaystyle \$1699.23

\displaystyle \$964.43

\displaystyle \$137.78

\displaystyle \$826.65

\displaystyle \$1010.35

Correct answer:

\displaystyle \$964.43

Explanation:

The most common way to do a problem like this is to begin by applying the first discount, calculating the amount to be removed from the original price. This is done by multiplying the original price by \displaystyle \small 0.3. This gives you \displaystyle 551.1. This is then subtracted from \displaystyle \small 1837 to give you \displaystyle \small 1285.9. Once again, this new number is multiplied, now by \displaystyle \small 0.25. This gives you \displaystyle \small 321.475. When subtracted from \displaystyle \small 1285.9, this gives you a final price of \displaystyle \small 964.425, or the rounded value of \displaystyle \small \small 964.43.

A simpler way to do this is to realize that the first price reduction makes the new price to be \displaystyle \small 70\% of the original. The second will then make the price to be \displaystyle \small 75\% of the intermediary price. Thus, you could easily compute:

\displaystyle \small \small 1837 * 0.7 * 0.75 = 964.425

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