SECTION 7.5 Applications of Rational Expressions 397
OBJECTIVE 3 Solve applications by using proportions.A ratiois a compar-
ison of two quantities. The ratio of ato bmay be written in any of the following ways.
ato b,orRatio of ato b
Ratios are usually written as quotients in algebra. A proportionis a statement that
two ratios are equal.
Proportiona
b
=
c
d
a
b
a:b,
Solving a ProportionIn 2008, about 15 of every 100 Americans had no health insurance. The population
at that time was about 302 million. How many million Americans had no health
insurance? (Source:U.S. Census Bureau.)
Step 1 Readthe problem.
Step 2 Assign a variable.Let the number of Americans (in millions) who had
no health insurance.
Step 3 Write an equation.The ratio 15 to 100 should equal the ratio xto 302.
Write a proportion.Step 4 Solve.
Simplify.x=45.3 Divide by 100.
4530 = 100 x
30,200a
15
100
b =30,200a
x
302
b
15
100
=
x
302
x=
EXAMPLE 4
Multiply by a common denom-
inator,. 100 # 302 =30,200Step 5 State the answer.There were 45.3 million Americans with no health
insurance in 2008.
Step 6 Checkthat the ratio of 45.3 million to 302 million equals 10015. NOW TRY
NOW TRY
EXERCISE 3
Solve for N.
NR
N-n=tNOW TRY
EXERCISE 4
In 2008, about 13 of every 100
Americans lived in poverty.
The population at that time
was about 302 million. How
many Americans lived in
poverty in 2008? (Source:
U.S. Census Bureau.)
NOW TRY ANSWERS
3.
4.39.26 million
N=tnt-RSolving a Formula for a Specified VariableSolve for n.
Multiply byDistributive property on the left
Subtract nrI.
Factor out n.