Percent Problems Help

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By — McGraw-Hill Professional
Updated on Sep 22, 2011

Percent Problems

Percent word problems can be done using the circle. In the lower left section place the rate or percent . In the lower right section place the base or whole , and in the upper section, place the part (see Fig. 6-12 ).

Word Problems

Fig. 6-12.

  • In order to solve a percent problem:
  • Step 1 Read the problem .
  • Step 2 Identify the base, rate (%), and part. One will be unknown .
  • Step 3 Substitute the values in the circle .
  • Step 4 Perform the correct operation: i.e., either multiply or divide .


Example 1

On a test consisting of 40 problems, a student received a grade of 95%. How many problems did the student answer correctly?

Solution 1

Place the rate, 95%, and the base, 40, into the circle (see Fig. 6-13 ).

Word Problems

Fig. 6-13.

Change 95% to 0.95 and multiply 0.95 × 40 = 38. Hence, the student got 38 problems correct.

Example 2

A football team won 9 of its 12 games. What percent of the games played did the team win?

Solution 2

Place the 9 in the "part" section and the 12 in the "base" section of the circle (see Fig. 6-14 ).

Word Problems

Fig. 6-14.

Then divide Word Problems Hence, the team won 75% of its games.

Example 3

The sales tax rate in a certain state is 6%. If sales tax on an automobile was $1,110, find the price of the automobile.

Solution 3

Place the 6% in the "rate" section and the $1,110 in the "part" section (see Fig. 6-15 ).

Word Problems

Fig. 6-15.

Change the 6% to 0.06 and divide: $1,110 ÷ 0.06 = $18,500. Hence, the price of the automobile was $18,500.

Percent Increase and Decrease Word Problems

Another type of percent problem you will often see is the percent increase or percent decrease problem. In this situation, always remember that the old or original number is used as the base.

Example 4

A coat that originally cost $150 was reduced to $120. What was the percent of the reduction?

Solution 4

Find the amount of reduction: $150 – $120 = $30. Then place $30 in the "part" section and $150 in the "base" section of the circle. $150 is the base since it was the original price (see Fig. 6-16 ).

Word Problems

Fig. 6-16.

Divide Word Problems = ÷ 150 = 0.20. Hence, the cost was reduced 20%.

Percent Word Problems Practice Problems


  1. A person bought an item at a 15% off sale. The discount was $90. What was the regular price?
  2. In an English Composition course which has 60 students, 15% of the students are mathematics majors. How many students are math majors?
  3. A student correctly answered 35 of the 40 questions on a mathematics exam. What percent did she answer correctly?
  4. A car dealer bought a car for $1500 at an auction and then sold it for $3500. What was the percent gain on the cost?
  5. An automobile service station inspected 215 vehicles, and 80% of them passed. How many vehicles passed the inspection?
  6. The sales tax rate in a certain state is 7%. How much tax would be charged on a purchase of $117.50?
  7. A person saves $200 a month. If her annual income is $32,000 per year, what percent of her income is she saving?
  8. A house sold for $80,000. If the salesperson receives a 4% commission, what was the amount of his commission?
  9. If the markup on a microwave oven is $42 and the oven sold for $98, find the percent of the markup on the selling price.
  10. A video game which originally sold for $40 was reduced $5. Find the percent of reduction.


  1. $600
  2. 9
  3. 87.5%
  4. Word Problems
  5. 172
  6. $8.23
  7. 7.5%
  8. $3200
  9. 42.86%
  10. 12.5%

Practice problems for these concepts can be found at: Percent Practice Test.

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