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Percent Equations

Equations to solve for rates, totals, and parts.

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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.

Watch This

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

Guidance

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

Rate is the ratio that the percent represents ( 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. is 25%, so we can use the second form of the equation: 25% of $80 is Part, or .

, 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 . 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 . Dividing both sides by 0.15, we get . So $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 part ($96) and the rate (12%, or 0.12). Using the rate equation, we get . Dividing both sides by 0.15, we get . 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. of

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.

Vocabulary

Percent Equation

Percent Equation

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

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