Basic Mathematics for College Students

682 Chapter 8 An Introduction to Algebra

EXAMPLE (^8) Playgrounds After
receiving a donation of 400 feet of chain
link fencing, the staff of a preschool
decided to use it to enclose a playground
that is rectangular. Find the length and the
width of the playground if the length is
three times the width.
Analyze

• The perimeter is 400 ft. Given


• The length is three times as long as the width. Given


• What is the length and what is the width of the rectangle? Find
  Form
  We will let wthe width of the playground. There is a second unknown quantity:
  the length of the playground. We look for a key phrase to help us decide how to
  represent it using an algebraic expression.
  Key phrase: length three timesthe width Translation: multiply width by 3
  So 3wthe length of the playground.
  The formula for the perimeter of a rectangle isP 2 l 2 w. In words, we can
  write

2  3 w  2  w  400

Solve

We need to isolate won the left side.

Do the multiplication: 2  3 w 6 w.

On the left side, combine like terms: 6w 2 w 8 w.

Do the division.

To find the second unknown, we substitute 50 for win the expression that

represents the length of the playground.

3 w3( 50 ) Substitute 50 for w.

This is the length of the playground.

State

The width of the playground is 50 feet and the length is 150 feet.

Check

If we add two lengths and two widths, we get 2(150) 2(50)  300  100 400.

Also, the length (150 ft) is three times the width (50 ft). The results check.

 150

w 50

To isolate w, divide both sides by 8 to undo the

(^) multiplication by 8.
8 w
8



400

8

8 w 400

6 w 2 w 400

2  3 w 2 w 400

the

perimeter.

is

the width of

the playground

the length of plus 2 

the playground

2 

The length is three times

as long as the width.

The perimeter is 400 ft. Width

1.476 units have been sold. 2.The tank originally contained 1,775 gallons of gasoline.

3.The student used to read 175 words per minute. 4.The quartet charged $340 for the

performance. 5.The student needs to complete 6 more 4-hour shifts of volunteer

service. 6.The couple made $570 at the yard sale. 7.His score on the interview was

70 and his score on the written part was 85. 8.The length of the lot is 225 feet and the

width of the lot is 175 feet.

ANSWERS TO SELF CHECKS

Self Check 8

CRIME SCENESPolice used

800 feet of yellow tape to fence

off a rectangular-shaped lot for

an investigation. Fifty less feet

of tape was used for each width

as for each length. Find the

length and the width of the lot.

Now TryProblem 26

50

(^8)  400
 40
00
 0
0