3.14: 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
Vocabulary
- A percent is simply a ratio with a base unit of 100—for example, .
- The percent equation is , or R% of Total is Part.
- The percent change equation is 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 . Dividing both sides by 0.15, we get . So $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
- of
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 .
Image Attributions
Description
Learning Objectives
Here you'll learn how to use the percent equation to find the rate, total, or part.