Beginning Algebra, 11th Edition

The amount painted by Joe in 1 hr plus the amount painted by Sam in 1 hr must

equal the amount they can do together. This relationship leads to the equation

Amount by Sam

Amount by Joe Amount together

Compare this equation with the one in Example 3.Multiplying each side by 15x

leads to

the same equation found in the third line of Step 4 in the example. The same solution

results.

5 x+ 3 x=15,

1

3

+

1

5

=

1

x

.

SECTION 7.7 Applications of Rational Expressions 471

Complete solution available
on the Video Resources on DVD

Concept Check Use Steps 2 and 3 of the six-step method to set up the equation you would

use to solve each problem. (Remember that Step 1 is to read the problem carefully.) Do not

actually solve the equation. See Example 1.

1.The numerator of the fraction is increased by an amount so that the value of the resulting

fraction is equivalent to. By what amount was the numerator increased?

(a)Let. (Step 2)

(b)Write an expression for “the numerator of the fraction is increased by an amount.”

(c)Set up an equation to solve the problem. (Step 3)

2.If the same number is added to the numerator and subtracted from the denominator of ,

the resulting fraction is equivalent to. What is the number?

(a)Let. (Step 2)

(b)Write an expression for “a number is added to the numerator of .” Then write an

expression for “the same number is subtracted from the denominator of .”

(c)Set up an equation to solve the problem. (Step 3)

Solve each problem. See Example 1.

3.In a certain fraction, the denominator is 6 more than the numerator. If 3 is added to both

the numerator and the denominator, the resulting fraction is equivalent to. What was the

original fraction (notwritten in lowest terms)?

4.In a certain fraction, the denominator is 4 less than the numerator. If 3 is added to both the

numerator and the denominator, the resulting fraction is equivalent to. What was the

original fraction?

5.The numerator of a certain fraction is four times the denominator. If 6 is added to both the

numerator and the denominator, the resulting fraction is equivalent to 2. What was the

original fraction (notwritten in lowest terms)?

6.The denominator of a certain fraction is three times the numerator. If 2 is added to the nu-

merator and subtracted from the denominator, the resulting fraction is equivalent to 1.

What was the original fraction (notwritten in lowest terms)?

7.One-third of a number is 2 greater than one-sixth of the same number. What is the number?

8.One-seventh of a number is 6 greater than the same number. What is the number?

3

2

5

7

23

12

23

12

x=

3

2

23

12

5

6

x=

13

3

5

6

7.7 EXERCISES