Solving Percent Word Problems

\(part = \% \ rate \times base\)

The key words in a percent equation will help you translate it into a correct algebraic equation. Remember the equal sign symbolizes the word "is" and the multiplication symbol symbolizes the word "of".

Example 1: Find 30% of 85.

Solution: You are asked to find the part of 85 that is 30%. First, translate into an equation.

\(n=30\% \times 85\)

Convert the percent to a decimal and simplify.

\( \begin{align*}n & =0.30 \times 85 \\ n & =25.5\end{align*}\)

Example 2: 50 is 15% of what number?

Solution: Translate into an equation.

\( 50 = 15\% \times w\)

Rewrite the percent as a decimal and solve.

\( \begin{align*}50 & = 0.15 \times w \\ \frac{50}{0.15} & = \frac{0.15 \times w}{0.15} \\ 333 \frac{1}{3} & = w\end{align*}\)