396 CHAPTER 7 Rational Expressions and Functions
OBJECTIVES
Applications of Rational Expressions
7.5
1 Find the value of an
unknown variable
in a formula.
2 Solve a formula for
a specified variable.
3 Solve applications
by using
proportions.
4 Solve applications
about distance,
rate, and time.
5 Solve applications
about work rates.OBJECTIVE 1 Find the value of an unknown variable in a formula. For-
mulas may contain rational expressions, as does and
1ƒ=
1p +
1t= q.
d
rNOW TRY
EXERCISE 1
Use the formula in Example 1
to find ƒ if and
q=10 cm.
p=50 cmNOW TRY
EXERCISE 2
Solve for m.
1
m-
2
n= 5
Finding the Value of a Variable in a FormulaIn physics, the focal length ƒ of a lens is given by the formula
In the formula, pis the distance
from the object to the lens and qis
the distance from the lens to the
image. See FIGURE 5. Find q if
and
LetMultiply by the LCD, 20q.Distributive propertyMultiply.
Subtract q.The distance from the lens to the image is 20 cm. NOW TRY
q= 20
2 q= q+ 20
20 q#
1
10
= 20 qa
1
20
b + 20 qa
1
q
b
20 q#
1
10
= 20 qa
1
20
+
1
q
b
ƒ=10,p=20.
1
10
=
1
20
+
1
q
1
ƒ
=
1
p
+
1
q
p=20 cm ƒ=10 cm.
1
ƒ
=
1
p
+
1
q
.
EXAMPLE 1
p qFocal Length of Camera Lens
FIGURE 5Solve this equation
for q.OBJECTIVE 2 Solve a formula for a specified variable.Recall that the goal
in solving for a specified variable is to isolate it on one side of the equals symbol.
Solving a Formula for a Specified VariableSolve for p.
1
ƒ
=
1
p
+
1
q
EXAMPLE 2
NOW TRY ANSWERS
1.^253 cm 2.m= 5 nn+ 2
Multiply by the LCD, ƒpq.Distributive property
Subtract ƒp.
Factor out p.p= Divide by q-ƒ. NOW TRY
ƒq
q-ƒ
p 1 q-ƒ 2 =ƒq
pq- ƒp=ƒq
pq=ƒq+ƒp
ƒpq#
1
ƒ
=ƒpqa
1
p
+
1
q
b
We want the
terms with pon
the same side.This is a key
step.