OBJECTIVE 3 Solve percent problems. An important everyday use of mathe-
matics involves the concept of percent. Percent is written with the symbol %. The
word percentmeans “per one hundred.” One percent means “one per one hundred”
or “one one-hundredth.”
1%0.01 or 1%
1
100
60 CHAPTER 2 Linear Equations, Inequalities, and Applications
Solving Percent Problems(a)A 50-L mixture of acid and water contains 10 L of acid. What is the percent of
acid in the mixture?
The given amount of the mixture is 50 L, and the part that is acid is 10 L. Let x
represent the percent of acid in the mixture.
partial amount
whole amount (base)The mixture is 20% acid.
(b)If a savings account balance of $4780 earns 5% interest in one year, how much
interest is earned?
Let xrepresent the amount of interest earned (that is, the part of the whole
amount invested). Since the equation is written as follows.
Multiply by 4780.The interest earned is $239. NOW TRY
x= 239
x=0.05 147802
partial amount a(^) base b =percent
x
4780
=0.05
5%=0.05,
x=0.20, or 20%
x=
10
50
EXAMPLE 6
Write as a decimal and
then a percent.Solving a Percent ProblemLet arepresent a partial amount of b, the base, or whole amount. Then the fol-
lowing equation can be used to solve a percent problem.
percent (represented as a decimal)
partial amount a
base b
For example, if a class consists of 50 students and 32 are males, then the percent
of males in the class is found as follows.
Let=0.64, or 64%
32
50 #2
2 =64= 100
64
100
a=32, b=50.
partial amount a
base b
=
32
50
NOW TRY
EXERCISE 6
Solve each problem.
(a)A 5-L mixture of water
and antifreeze contains 2 L
of antifreeze. What is the
percent of antifreeze in the
mixture?
(b)If a savings account earns
2.5% interest on a balance
of $7500 for one year,
how much interest is
earned?
NOW TRY ANSWERS
- (a)40% (b)$187.50