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.
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CK12 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 total is $80. ‘of’ means multiply. \begin{align*}R\%\end{align*}
\begin{align*}0.25 \times 80 = 20\end{align*}
Example B
Express $90 as a percentage of $160.
Solution
This time we are looking for the rate. We are given the part ($90) and the total ($160). Using the rate equation, we get \begin{align*}\text{Rate} \times 160 = 90\end{align*}
Example C
$50 is 15% of what total sum?
Solution
This time we are looking for the total. We are given the part ($50) and the rate (15%, or 0.15). Using the rate equation, we get \begin{align*}0.15 \times \text{Total} = \$50\end{align*}
Watch this video for help with the Examples above.
CK12 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*}
13%=13100 .  The percent equation is \begin{align*}\text{Rate} \times \text{Total} = \text{Part}\end{align*}
Rate×Total=Part , 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*}
Percent change=final amount  original amountoriginal amount×100%. 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 part ($96) and the rate (12%, or 0.12). Using the rate equation, we get \begin{align*}0.12 \times \text{Total} = \$96\end{align*}
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*}
y% of \begin{align*}3x\end{align*}3x
Texas Instruments Resources
In the CK12 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.