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Chapter 7—Percents

7-3 Solving Percent Problems

THIS SECTION IS CURRENTLY UNDER RECONSTRUCTION

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:

 P = a 100 b

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:

 P = a 100 b

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:
 P = a 100 b

Rearrange the proportion to solve for the percent, P:

 P = 100a b

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

Example

Problem:

50 is 20% of _____.

Procedure:

Use these values:

P = 20
a = 50
In this statement of proportion:
 P = a 100 b

Rearrange the proportion to solve for b:

 b = 100a P

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:
 P = a 100 b

Rearrange the proportion to solve for a:

 a = Pb 100

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

 P = a 100 b

This series of Examples & Exercises tests your ability to rearrange the equation and assign the correct values for basic percentage problems.

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