Intermediate Algebra (11th edition)

Pvaries directly as h.

Substitute 795.50 for Pand 43 for h.

Use a calculator.

Her hourly wage is $18.50, and Pand hare related by

P=18.50h.

k=18.50

795.50= 43 k

P=kh

408 CHAPTER 7 Rational Expressions and Functions

NOW TRY
EXERCISE 1
One week Morgan sold
8 dozen eggs for $20. How
much does she charge for
one dozen eggs?

NOW TRY
EXERCISE 2
For a constant height, the area
of a parallelogram is directly
proportional to its base. If the
area is when the base
is 4 cm, find the area when
the base is 7 cm.

20 cm^2

This is the constant

of variation.

We can use this equation to find her pay for any number of hours worked.

Solving a Direct Variation Problem

Hooke’s law for an elastic spring states that the distance a

spring stretches is directly proportional to the force applied.

If a force of 150 newtons* stretches a certain spring 8 cm,

how much will a force of 400 newtons stretch the spring? See

FIGURE 7.

If dis the distance the spring stretches and ƒ is the force

applied, then for some constant k. Since a force of

150 newtons stretches the spring 8 cm, we use these values to

find k.

Variation equation

Let and.

Solve for k.

Lowest terms

Substitute for kin the variation equation.

Here,.

For a force of 400 newtons, substitute 400 for ƒ.

Let.

The spring will stretch^643 cm,or 21 13 cm, if a force of 400 newtons is applied.

d= ƒ= 400

4

75

14002 =

64

3

d= k= 754

4

75

ƒ

754 d= kƒ

k=

4

75

k=

8

150

8 =k# 150 d= 8 ƒ= 150

d=kƒ

d= kƒ

EXAMPLE 2

*A newton is a unit of measure of force used in physics.

(^8) d
150
400
FIGURE 7
NOW TRY ANSWERS

1. $2.50 2.35 cm^2

NOW TRY

NOW TRY

Solving a Variation Problem

Step 1 Write the variation equation.

Step 2 Substitute the initial values and solve for k.

Step 3 Rewrite the variation equation with the value of kfrom Step 2.

Step 4 Substitute the remaining values, solve for the unknown, and find the

required answer.