Solving Percent Word Problems

A percent is a ratio whose denominator is 100. Before we can use percent to solve problems, let's review how to convert percents to decimals and fractions and vice versa.

To convert a decimal to a percent, multiply the decimal by 100.

Example: Convert 0.3786 to a percent.

\( \begin{align*}0.3786 \times 100=37.86\%\end{align*}\)

To convert a percentage to a decimal, divide the percentage by 100.

Example: Convert 98.6% into a decimal.

\( \begin{align*}98.6 \div 100 = 0.986\end{align*}\)

When converting fractions to percent, we can substitute \( \frac{x}{100}\) for \(x\%\), where \(x\) is the unknown.

Example: Express \( \dfrac{3}{5}\) as a percent.

We start by representing the unknown as \(x\%\) or \(\frac{x}{100}\).

\( \begin{align*}\left (\frac{3}{5} \right) & = \frac{x}{100} && \text{Cross multiply}. \\ 5x & = 100 \cdot 3 \\ 5x & = 300 \\ x & = \frac{300}{5} = 60 && \text{Divide both sides by}\ 5\ \text{to solve for}\ x. \\ \left (\frac{3}{5} \right) & = 60\%\end{align*}\)

Now that you remember how to convert between decimals and percents, you are ready for the Percent Equation.

Source: cK-12, https://www.ck12.org/book/basic-algebra/section/3.7/
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