**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 ).

*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*.

**Examples**

**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 ).

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 ).

Then divide 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 ).

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 ).

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

**Percent Word Problems Practice Problems**

**Practice**

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

**Answers**

- $600
- 9
- 87.5%
- 172
- $8.23
- 7.5%
- $3200
- 42.86%
- 12.5%

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

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