How to Solve Any Percent Problem

Percent means per 100, so 20% is the decimal 0.20. Most problems fit this equation:

percent \times whole = part

Decide which of the three values is missing, then solve.

Find the part: what is 20% of 60?

$0.20 \times 60 = 12$

Find the percent: 15 is what percent of 60?

$p \times 60 = 15$

$p = \frac{15}{60} = 0.25$ , which is 25%.

Find the whole: 12 is 30% of what number?

$0.30 \times w = 12$

$w = \frac{12}{0.30} = 40$

Percent change

percent change = \frac{new - old}{old}

A price goes from $50 to $65. What is the percent increase?

$\frac{65 - 50}{50} = \frac{15}{50} = 0.30$ , which is a 30% increase.

Common mistake

A 20% increase followed by a 20% decrease gets you back to the start.

Start at 100. After the increase you have 120. A 20% decrease is 20% of 120, which is 24, so you end at 96. The two percents are taken from different wholes.

Try it yourself

What is 35% of 80?
Show answer
28
18 is what percent of 72?
Show answer
25%
A value drops from 30 to 24. What is the percent decrease?
Show answer
20%