Basic Mathematics for College Students

Chapter 8 Summary and Review 703

The five-step problem-solving strategy can be
used to solve application problems to find two
unknowns.

SOUND SYSTEMS A 45-foot-long speaker wire is cut into two

pieces. One piece is 9 feet longer than the other. Find the length of

each piece of wire.

Analyze

• A 45-foot long wire is cut into two pieces. Given


• One piece is 9 feet longer than the other. Given


• What is the length of the shorter piece and the
  length of the longer piece of wire? Find

Form

Since we are told that the length of the longer piece of wire is related

to the length of the shorter piece,

Let x the length of the shorter piece of wire

There is a second unknown quantity. Look for a key phrase to help

represent the length of the longer piece of wire using an algebraic

expression.

Key Phrase:9 feet longer Translation:addition

So x+ 9 = the length of the longer piece of wire

Now, translate the words of the problem to an equation

is

x  x 9  45

Solve

We need to isolate xon the left side.

Combine like terms: xx 2 x.

To isolate 2x, subtract 9 from both sides.

Do the subtraction.

To isolate x, undo the multiplication by 2 by

dividing both sides by 2.

Do the division.

To find the second unknown, we substitute 18 for xin the expression

that represents the length of the longer piece of wire.

x 9  18  9  27

State

The length of the shorter piece of wire is 18 feet and the length of the

longer piece is 27 feet.

x 18

2 x

2



36

2

2 x 36

2 x 9  9  45  9

2 x 9  45

xx 9  45

45 feet.

the length of

the longer piece

The length of the plus

shorter piece