Basic Mathematics for College Students

Solve application problems to find two unknowns.

When solving application problems, we usually let the variable stand for the quantity

we are asked to find. In the next two examples, each problem contains a second

unknown quantity. We will look for a key word or phrase in the problem to help us

describe it using an algebraic expression.

2

680 Chapter 8 An Introduction to Algebra

Self Check 6

YA R D S A L E SA husband and wife

split the money equally that they

made on a yard sale. The

husband gave $75 of his share to

charity, leaving him with $210.

How much money did the couple

make at their yard sale?

Now TryProblem 24

EXAMPLE (^6) Attorney’s Fees In return for her services, an attorney
and her client split the jury’s cash award equally. After paying her assistant $1,000,
the attorney ended up making $10,000 from the case. What was the amount of the
award?
Analyze

• The attorney and client split the award equally. Given


• The attorney’s assistant was paid $1,000. Given


• The attorney made $10,000. Given


• What was the amount of the award? Find
  Form
  Let xthe amount of the award. Two key phrases in the problem help us form an
  equation.
  Key phrase: split the award equally Translation: divide by 2
  Key phrase: paying her assistant$1,000 Translation: subtract $1,000
  Now we translate the words of the problem into an equation.

 1,000  10,000

Solve

We need to isolate x on the left side.

To isolate the variable term ,

add 1,000 to both sides to

undo the subtraction of 1,000.

Do the addition.

Do the multiplication.

State

The amount of the award was $22,000.

Check

If the award of $22,000 is split in half, the attorney’s share is $11,000. If $1,000 is

paid to her assistant, we subtract to get:

This is what the attorney made.

The result, $22,000, checks.



$11,000

1,000

$10,000

x22,000

To isolate the variable x,

multiply both sides by 2

to undo the division by 2.

2 

x

2

 2 11,000

x

2

11,000

x

2

x

2

1,0001,00010,0001,000

x

2

1,00010,000

x

2

the amount the

attorney makes.

is

the amount

paid to the

assistant

minus

The award

split in half

11,000

 2

22,000