Training Percents Solving Percent Problems
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Solving Percent Problems

22 min Percents

The Three Types of Percent Problems

Solving percent problems is one of the most practical skills in all of mathematics. From calculating tips and taxes to understanding interest rates and statistics, percent calculations show up constantly in everyday life.

Every basic percent problem can be reduced to one of three types: finding the part, finding the whole, or finding the percent. The proportion method — part over whole equals percent over 100 — handles all three elegantly.

This lesson teaches you both the proportion method and the equation method, giving you two powerful tools for any percent problem you encounter.

Every percent problem involves three quantities: the part, the whole (base), and the percent.

The Percent Equation

$$\text{Part} = \text{Percent} \times \text{Whole}$$

or equivalently: $\;\dfrac{\text{Part}}{\text{Whole}} = \dfrac{\text{Percent}}{100}$

Type 1 — Find the Part

"What is 15% of 200?"

Example 1

What is $15\%$ of $200$?

$$\text{Part} = 0.15 \times 200 = 30$$

Example 2

What is $8.5\%$ of $400$?

$$0.085 \times 400 = 34$$

Type 2 — Find the Percent

"12 is what percent of 80?"

Example 3

$12$ is what percent of $80$?

$$\frac{12}{80} = 0.15 = 15\%$$

Example 4

$7$ is what percent of $28$?

$$\frac{7}{28} = 0.25 = 25\%$$

Type 3 — Find the Whole

"45 is 30% of what number?"

Example 5

$45$ is $30\%$ of what number?

$$\text{Whole} = \frac{45}{0.30} = 150$$

Example 6

$18$ is $120\%$ of what number?

$$\text{Whole} = \frac{18}{1.20} = 15$$

Tip

The word "of" in percent problems signals multiplication. The word "is" signals equals.

Practice Problems

1. What is $25\%$ of $360$?
2. $18$ is what percent of $72$?
3. $56$ is $40\%$ of what number?
4. What is $150\%$ of $80$?
5. $9$ is what percent of $45$?
6. $33$ is $110\%$ of what number?
7. What is $6.5\%$ of $200$?
8. $35$ is what percent of $50$?
9. $60$ is $75\%$ of what number?
10. What is $0.5\%$ of $600$?
11. $15$ is what percent of $12$?
12. What is $12\%$ of $\$1{,}250$?
13. $\$42$ is $7\%$ of what price?
14. What is $33\dfrac{1}{3}\%$ of $81$?
15. $105$ is $70\%$ of what number?
Show Answer Key

1. $90$

2. $25\%$

3. $140$

4. $120$

5. $20\%$

6. $30$

7. $13$

8. $70\%$

9. $80$

10. $3$

11. $125\%$

12. $\$150$

13. $\$600$

14. $27$

15. $150$

Percent–Fraction–Decimal Conversions Percent Change and Applications