OBJECTIVE 5 Solve percent problems.Recall from Section 2.2that percent
means “per one hundred,” so 5% means 0.05, 14% means 0.14, and so on.
Solving a Percent ProblemIn 2006, total annual health expenditures in the United States were about $2000 billion
(or $2 trillion). This was an increase of 180% over the total for 1990. What were the
approximate total health expenditures in billions of dollars in the United States in
1990? (Source:U.S. Centers for Medicare & Medicaid Services.)
Step 1 Readthe problem. We are given that the total health expenditures increased
by 180% from 1990 to 2006, and $2000 million was spent in 2006. We must
find the expenditures in 1990.
Step 2 Assign a variable.Let xrepresent the total health expenditures for 1990.
so 1.8xrepresents the additional expenditures since 1990.
Step 3 Write an equationfrom the given information.
the expenditures in 1990 the increase 2000x + 1.8x = 2000
+ =180 % = 1801 0.01 2 = 1.8,
EXAMPLE 5
SECTION 2.3 Applications of Linear Equations 71
NOW TRY
EXERCISE 5
In the fall of 2009, there were
96 Introductory Statistics stu-
dents at a certain community
college, an increase of 700%
over the number of Introduc-
tory Statistics students in the
fall of 1992. How many Intro-
ductory Statistics students
were there in the fall of 1992?
NOW TRY ANSWER
- 12
Note the x
in 1.8x.Step 4 Solvethe equation.
Identity property
Combine like terms.
Divide by 2.8.Step 5 State the answer.Total health expenditures in the United States for 1990
were about $714 billion.
Step 6 Checkthat the increase, is about 180% of 714.
NOW TRY2000 - 714 =1286,
xL 714
2.8x= 2000
1 x+1.8x= 2000
CAUTION Avoid two common errors that occur in solving problems like the
one in Example 5.
1. Do not try to find 180% of 2000 and subtract that amount from 2000. The 180%
should be applied to the amount in 1990, not the amount in 2006.
2. Do not write the equation as
Incorrect