Solving Percent Equations

The percent equation has three parts: percent (P), amount (A), and base (B).

"P % of B is A" is the basic form of the percent equation. This can be written algebraically as

0.01P \times A = B

The following three examples show how the percent equation can be used to solve basic percent problems:

Example 1 : What is 20% of 18?

Solution: Write this out algebraically.

Convert 20% to decimal form:

20% = 0.2

The basic equation is A = 0.2 x 18

Solve for A:

A = 3.6

20% of 18 is 3.6.

Example 2: What percent of 54 is 9?

Solution: Write this out algebraically.

Let P represent the percent.

The basic equation is 0.01P x 54 = 9

Simplify the left side of the equation:

0.54P = 9

Solve for P:

P = \frac{9}{0.54} = \frac{900}{54} = \frac{50}{3} = 16\frac{2}{3}

16\frac{2}{3} of 54 is 9.

Example 3: 18 is 25% of what number?

Solution: Write this out algebraically.

Convert 25% to decimal form:

25% = 0.25

The basic equation is 18 = 0.25 x B

Solve for B:

B = B = \frac{18}{0.25} = 72

18 is 25% of 72.

What is 40% of 90?
85% of what number is 204?
What percent of 90 is 13.5?