What if you knew that 25% of a number was equal to 24? How could you find that number? After completing this Concept, you'll be able to use the percent equation to solve problems like this one.

### Watch This

CK-12 Foundation: 0314S The Percent Equation (H264)

### Guidance

The percent equation is often used to solve problems. It goes like this:

\begin{align*}& \text{Rate} \times \text{Total} = \text{Part}\\
& \qquad \qquad \text{or}\\
& R\% \ \text{of Total is Part}\end{align*}

** Rate** is the ratio that the percent represents (\begin{align*}R\%\end{align*}

** Total** is often called the

**.**

*base unit*** Part** is the amount we are comparing with the base unit.

#### Example A

*Find 25% of $80.*

**Solution**

We are looking for the ** part**. The

**is $80. ‘of’ means multiply. \begin{align*}R\%\end{align*}**

*total*\begin{align*}0.25 \times 80 = 20\end{align*}**$20**.

#### Example B

*Express $90 as a percentage of $160.*

**Solution**

This time we are looking for the ** rate**. We are given the

**($90) and the**

*part***($160). Using the rate equation, we get \begin{align*}\text{Rate} \times 160 = 90\end{align*}**

*total*#### Example C

*$50 is 15% of what total sum?*

**Solution**

This time we are looking for the ** total**. We are given the

**($50) and the**

*part***(15%, or 0.15). Using the rate equation, we get \begin{align*}0.15 \times \text{Total} = \$50\end{align*}**

*rate***$50 is 15% of $333.33.**

Watch this video for help with the Examples above.

CK-12 Foundation: The Percent Equation

### Guided Practice

*$96 is 12% of what total sum?*

**Solution:**

This time we are looking for the ** total**. We are given the

**($96) and the**

*part***(12%, or 0.12). Using the rate equation, we get \begin{align*}0.12 \times \text{Total} = \$96\end{align*}**

*rate***$96 is 12% of $800.**

### Explore More

Find the following.

- 30% of 90
- 27% of 19
- 16.7% of 199
- 11.5% of 10.01
- 0.003% of 1,217.46
- 250% of 67
- 34.5% of y
- 17.02% of y
- x% of 280
- a% of 0.332
- \begin{align*}y\%\end{align*}
y% of \begin{align*}3x\end{align*}3x

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 3.14.

### Texas Instruments Resources

*In the CK-12 Texas Instruments Algebra I FlexBook® resource, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9613.*