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3.14: Percent Equations

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

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.

CK-12 Foundation: The Percent Equation

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.

Practice

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, 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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Difficulty Level:

At Grade

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Date Created:

Aug 13, 2012

Last Modified:

Sep 26, 2014
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