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Percent Equations

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Practice Percent Equations
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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.

Guidance

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

$& \text{Rate} \times \text{Total} = \text{Part}\\& \qquad \qquad \text{or}\\ & R\% \ \text{of Total is Part}$

Rate is the ratio that the percent represents ( $R\%$ 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 total is$80. ‘of’ means multiply. $R\%$ is 25%, so we can use the second form of the equation: 25% of $80 is Part, or $0.25 \times 80 = \text{Part}$ . $0.25 \times 80 = 20$ , 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 part ($90) and the total ($160). Using the rate equation, we get $\text{Rate} \times 160 = 90$ . Dividing both sides by 160 tells us that the rate is 0.5625, or 56.25%.

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 $0.15 \times \text{Total} = \50$ . Dividing both sides by 0.15, we get $\text{Total} = \frac{50}{0.15} \approx 333.33$ . So $50 is 15% of$333.33.

Watch this video for help with the Examples above.

Vocabulary

• A percent is simply a ratio with a base unit of 100—for example, $13\% = \frac{13}{100}$ .
• The percent equation is $\text{Rate} \times \text{Total} = \text{Part}$ , or R% of Total is Part.
• The percent change equation is $\text{Percent change} = \frac{\text{final amount - original amount}}{\text{original amount}} \times 100\%.$ 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 $0.12 \times \text{Total} = \96$ . Dividing both sides by 0.15, we get $\text{Total} = \frac{96}{0.12}=800$ . So $96 is 12% of$800.

Explore More

Find the following.

1. 30% of 90
2. 27% of 19
3. 16.7% of 199
4. 11.5% of 10.01
5. 0.003% of 1,217.46
6. 250% of 67
7. 34.5% of y
8. 17.02% of y
9. x% of 280
10. a% of 0.332
11. $y\%$ of $3x$

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 .

Vocabulary Language: English

Percent Equation

Percent Equation

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