Basic Mathematics for College Students

To solve percent application problems, we often have to rewrite the facts of the

problem in percent sentence form before we can translate to an equation.

526 Chapter 6 Percent

Self Check 8

150 is of what number?

Now TryProblems 43 and 83

66 23 %

To undo the multiplication by 3 and isolate xon the right side, divide

both sides of the equation by 3. Then remove the common factor of

3 from the numerator and denominator.

On the left side, divide 24 by 3.

Thus, 6 is 75% of 8. That is, there are 8 members on the State Board of Examiners

mentioned in the newspaper article.

8 x

24

3



x 3

1

3

1







 

EXAMPLE (^8) 31.5 is 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 write the mixed number as the
improper fraction.
Write as.
To solve the proportion, find the cross products:

. Then set them equal.

To simplify the left side of the equation, do the

multiplication: 31.5  100 3,150.

To undo the multiplication by and isolate xon the right

side, divide both sides of the equation by. Then remove

the common factor of from the numerator and

denominator.

On the left side, the fraction bar indicates division.

On the left side, write 3,150 as a fraction:. Then use

the rule for dividing fractions: Multiply by the reciprocal of

, which is.

Multiply the numerators.

Multiply the denominators.

Divide 9,450 by 100 by moving the understood decimal

point in 9,450 two places to the left.

Thus, 31.5 is 3313 %of 94.5.

94.50x

9,450

100

x

1003 1003

3,150 1

3,150

1



3

100

x

3,150

100

3

x

1003

1003

1003

3,150

100

3



x

100

3

1

100

3

1

3,150x

100

3

31.5

x



100

3

100

31.5 100 x

100

3

33 31 1003

31.5

x



100

3

100

1003

33 13

31.5

x



33

1

3

100

amount percent base

31.5 33 13 % what number?

amountbase percent 100

33 13 %