Page 484 - Basic College Mathematics with Early Integers

S E C T I O N 6.3 I SOLVING PERCENT PROBLEMS USING PROPORTIONS 461

Example 5 Translate to a proportion. PRACTICE 5

What percent of 30 is 75? Translate to a proportion.What
percent of 50 is 65?
t
T T T
Solution: percent base amount

75 p
=
30 100
Work Practice 5

Example 6 Translate to a proportion. PRACTICE 6
Translate to a proportion. 36%
45% of 105 is what number?
of 80 is what number?
t
T T T
Solution: percent base amount
a 45
=
105 100
Work Practice 6

Objective Solving Percent Problems

The proportions that we have written in this section contain three values that can
change: the percent, the base, and the amount. If any two of these values are known,
we can find the third (the unknown value).To do this, we write a percent proportion
and find the unknown value as we did in Section 5.3.

Example 7 Solving Percent Proportion for the Amount PRACTICE 7
What number is 8% of 120?
What number is 30% of 9?

t
T T T
Solution: amount percent base

a 30
=
9 100
To solve, we set cross products equal to each other. The proportion in
Example 7 contains the ratio
30
a = 30 . A ratio in a proportion
9 100 100
may be simplified before
solving the proportion. The
#
#
a 100 = 9 30 Set cross products equal. unknown number in both
#
a 100 = 270 Multiply. a 30 a 3
= and = is 2.7
9 100 9 10
Recall from Section 5.3 that if “some number times 100 is 270,” then the number
is 270 divided by 100.
270
a = Divide 270 by 100, the number multiplied by a.
100
a = 2.7 Simplify. Answers
65 p a 36
Thus, 2.7 is 30% of 9. 5. = 6. =
50 100 80 100
Work Practice 7 7. 9.6