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# Percent Equations

## Equations to solve for rates, totals, and parts.

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Practice Percent Equations
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Percent Equations

Suppose that there was an article in your school newspaper that said that 80% of the students in your school plan on attending the prom. It also said that 500 students in your school plan on attending the prom. Would you be able to tell from this information how many students there are in your school?

### Percent Equations

Now that you remember how to convert between decimals and percents, you are ready for the percent equation:

\begin{align*}part = \% \ rate \times base\end{align*}

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".

#### Let's solve the following percent problems:

1. Find 30% of 85.

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

\begin{align*}n=30\% \times 85\end{align*}

Convert the percent to a decimal and simplify:

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

1. A dime is worth what percent of a dollar?

Since a dime is 10 cents and a dollar is 100 cents, we can set up the following equation:

\begin{align*}\frac{10}{100}=10\%\end{align*}

1. 50 is 15% of what number?

Translate into an equation:

\begin{align*}50 = 15\% \times w\end{align*}

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*}

### Examples

#### Example 1

Earlier, you were asked how many students attend your school if 80% of the students are attending prom and there are 500 students attending prom.

For the percent equation, this problem gives us the rate and the part. We need to solve for the base, call it \begin{align*}x\end{align*}.

The percent equation is:

\begin{align*}500 = 80\text{%}\times x\end{align*}

Using the fractional form of the percentage, we can solve this equation for \begin{align*}x\end{align*}:

\begin{align*}500 = \frac{80}{100}\times x\\ \frac{100}{80}\times 500 = \frac{100}{80}\times \frac{80}{100}\times x\\ \frac{50000}{80} = x\\ 625 = x\end{align*}

#### Example 2

6 is 2% of what number?

First, use the percent equation:

\begin{align*}6=2\% \times n\end{align*}

Like Example 1, we should use the fractional form of a percentage. Substitute in \begin{align*}\frac{2}{100}\end{align*} for 2%, since they are equivalent expressions:

\begin{align*} & 6= \frac{2}{100} \times n\\ &\frac{100}{2}\times 6=\frac{100}{2} \times \frac{2}{100} \times n\\ &\frac{600}{2}= n\\ & 300 = n\\ \end{align*}

6 is 2% of 300.

### Review

1. 32% of 600 is what number?
2. 50% of 9.00 is what number? 3. \begin{align*}\frac{3}{4}\%\end{align*} of 16 is what number? 4. 9.2% of 500 is what number 5. 8 is 20% of what number? 6. 99 is 180% of what number? 7. What percent of 7.2 is 45? 8. What percent of 150 is 5? 9. What percent of 50 is 2500? 10.3.50 is 25% of what number?

To see the Review answers, open this PDF file and look for section 3.10.

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### Vocabulary Language: English Spanish

Percent Equation

The percent equation can be stated as: "Rate times Total equals Part," or "R% of Total is Part."