# 3.14: Percent Equations

**At Grade**Created by: CK-12

**Practice**Percent Equations

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*} in the second version).

** 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*} is 25%, so we can use the second form of the equation: 25% of $80 is Part, or \begin{align*}0.25 \times 80 = \text{Part}\end{align*}.**

*total*
\begin{align*}0.25 \times 80 = 20\end{align*}, so the Part we are looking for is **$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*}. Dividing both sides by 160 tells us that the rate is 0.5625, or 56.25%.**

*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*}. Dividing both sides by 0.15, we get \begin{align*}\text{Total} = \frac{50}{0.15} \approx 333.33\end{align*}. So**

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

Watch this video for help with the Examples above.

CK-12 Foundation: The Percent Equation

### Vocabulary

- A
**percent**is simply a ratio with a base unit of 100—for example, \begin{align*}13\% = \frac{13}{100}\end{align*}. - The
**percent equation**is \begin{align*}\text{Rate} \times \text{Total} = \text{Part}\end{align*}, or R% of Total is Part. - The percent change equation is \begin{align*}\text{Percent change} = \frac{\text{final amount - original amount}}{\text{original amount}} \times 100\%.\end{align*} A
**positive**percent change means the value**increased**, while a**negative**percent change means the value**decreased**.

### 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*}. Dividing both sides by 0.15, we get \begin{align*}\text{Total} = \frac{96}{0.12}=800\end{align*}. So**

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

### Practice

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*} of \begin{align*}3x\end{align*}

### Texas Instruments Resources

*In the CK-12 Texas Instruments Algebra I FlexBook, 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.*

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### Image Attributions

Here you'll learn how to use the percent equation to find the rate, total, or part.