Basic Mathematics for College Students

6.2 Solving Percent Problems Using Percent Equations and Proportions 523

Self Check 3

What number is 240% of 80.3?

Now TryProblem 23







1

4

5

6

.8

 8

126.4

3 Solve percent proportions to find the percent.

Recall the drinking water problem from the newspaper example in the introduction
to this section. We can write and solve a percent proportion to find the unknown
percent.

Self Check 4

4 is what percent of 80?

Now TryProblems 27 and 79







EXAMPLE (^4) 38 is what percent of 40?
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 percent.
SolutionFirst, we write the percent proportion.
is of
This is the proportion to solve.

38

40



x

100

amount percent base

38 what percent 40?

amountbase percent 100

Circulation Monday, March 23 50 cents

Transit Strike Averted!

Drinking Water38 of 40 Wells

Declared Safe

500-member unionLabor: 84% of

votes to acceptnew offer

New Appointees

These six area residentsnow make up 75% of the

State Board of Examiners

 

EXAMPLE (^3) What number is 160% of 15.8?
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
This is the proportion to solve.
To make the calculations easier, it is helpful to simplify the ratio at this time.
On the right side, simplify:.
Find the cross products:.
Then set them equal.
To simplify the right side of the equation, do the
multiplication: 15.8  8 126.4.
To undo the multiplication by 5 and isolate x
on the left side, divide both sides of the equation
by 5. Then remove the common factor of 5 from
the numerator and denominator.
On the right side, divide 126.4 by 5.
Thus, 25.28 is 160% of 15.8.
x25.28
x 5
1
5
1



126.4

5

x 5 126.4

x 5 15.8 (^8) 15.8x  58
160
100

8  20
1
5  (^201)

8
5
x
15.8



8

5

160100

x

15.8



160

100

amount percent base

What number 160% 15.8?

amountbase percent 100

25.28

(^5)  126.40
 10
26
 25
14
 10
40
 40
0