Basic Mathematics for College Students

 

6.2 Solving Percent Problems Using Percent Equations and Proportions 525

4 Solve percent proportions to find the base.

Recall the State Board of Examiners problem from the newspaper example in the
introduction to this section. We can write and solve a percent proportion to find the
unknown base.

Self Check 7

3 is 5% of what number?

Now TryProblem 39







 

125

6  750

 6

15

 12

30

 30

0

EXAMPLE (^7) 6 is 75% of what number?
StrategyWe will identify the percent, the base, and
the amount and write a percent proportion of the form
.
WHYThen we can solve the proportion to find the
unknown number.
SolutionFirst, we write the percent proportion.
is of
To make the calculations easier, it is helpful to simplify the ratio at this time.
Simplify:.
To solve the proportion, find the cross products:.
Then set them equal.
To simplify the left side of the equation, do the multiplication:
6  4 24.
24 x 3
6
x
3
6  4 x 3 4
75
100

3  25
1
4  25
1

3
4

6

x



3

4

10075

6

x



75

100

amount percent base

6 75% what number?

amountbase percent 100

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SolutionFirst, we write the percent proportion.

of is

This is the proportion to solve.

To solve the proportion, find the cross products:.

Then set them equal.

To simplify the left side of the equation, do the

multiplication: 7.5  100 750.

To undo the multiplication by 6 and isolate x

on the right side, divide both sides of the equation

by 6. Then remove the common factor of 6 from

the numerator and denominator.

On the left side, divide 750 by 6.

Thus, 7.5 is 125% of 6.

125 x

750

6



6

1

x

6

1

750  6 x

7.5

6 

x

7.5 100  6 x 100

7.5

6



x

100

percent base amount

What percent 6 7.5?