top
Chapter 7—Percents
7-3 Solving Percent Problems
THIS SECTION IS CURRENTLY UNDER RECONSTRUCTION
PLEASE EXCUSE THE CONFUSION
This lesson demonstrates two ways to approach the solution of all kinds of percent problems -- the kinds of problems you find in everyday commerce, the news, health and nutrition, technical issues, and just about any other area of your life and culture. Just about anywhere there is a need to communicate amounts and differences in amounts. That covers a lot of personal and working life.
Solving Percents by Proportions
| Equation The ratio/proportion equation for all basic percentage problems is: where: - P is the percent
- a is the partial amount
- b is the whole amount
|
Solving Percents by the Percent Equation
The ratio/proportion equation for all basic percentage problems is:
where:
- P is the percent
- a is one of the two value
- b is the second values
Example
Problem:
60 is what percent of 180?
Procedure:
Use these values:
- a = 60
- b = 180
- In this statement of proportion:
Rearrange the proportion to solve for the percent, P:
Substitute the known values and solve the equation:
| P = | 100a | = | 100 x 60 | = 33.3 |
| b | 180 |
Solution:
60 is 33.3% of 180
Examples & Exercises
| Check your understand and build your confidence with these examples/exercises | |
| Example Problem: 50 is 20% of _____. Procedure: Use these values: - P = 20
- a = 50
- In this statement of proportion:
Rearrange the proportion to solve for b: Substitute the known values and solve the equation: | b= | 100a | = | 100 x 50 | = 250 | | P | 20 | Solution: 50 is 20% of 250 | Important In this example, how do you know whether to assign the given value of 50 to variable a or to variable b? You can see the example works out by setting a = 50 and solving for b. But how do you know your aren't supposed to let b = 50 and solve for a? Look at it this way: When we see a statement such as 50 is 20% of something, it figures that the "something" is going to be larger than 50. Why? Because 50 is only 20% of some larger value. Now when you look at a ratio such as a/b, the larger value has to be the denominator--in order for the ratio to be less than 1, or 0.2 in this example. |
| |
Examples & Exercises
| Master the idea with these examples/exercises | |
Example
Problem:
18% of 240 is ______
Procedure:
Use these values:
- p = 18
- b = 240
- In this statement of proportion:
Rearrange the proportion to solve for a:
Substitute the known values and solve the equation:
| a = | Pb | = | 18 x 240 | = 43.2 |
| 100 | 100 |
Solution:
18% of 240 is 43.2
Examples & Exercises
| Build your skills with these exercises. | |
Section Review
Examples & Exercises
| This series of Examples & Exercises tests your ability to rearrange the equation and assign the correct values for basic percentage problems. | |
