Pre-Algebra Demystified

EXAMPLE

A carpenter cuts a board 72 inches long into two pieces. One piece is twice as

long as the other. Find the lengths of the pieces.

SOLUTION

Step 1 Let x¼the length of the smaller piece

Let 2x¼the length of the larger piece

Step 2 xþ2x¼ 72

Step 3 xþ2x¼ 72

3x¼ 72

3 x

3

¼

72

3

x¼24 inches

2x¼ 2  24 ¼48 inches

Hence, one piece is 24 inches long and the other piece is 48 inches long.

Step 4 Check: 24 inchesþ48 inches¼72 inches

EXAMPLE

$40 in tips is to be divided among three food servers. The first server gets

twice as much as the second server since he worked twice as long; the third

server gets $7. Find the amount each server received.

SOLUTION

Step 1 Let x¼the amount the second server receives

Let 2x¼the amount the first server received

Step 2 xþ2xþ 7 ¼ 40

3xþ 7 ¼ 40

3xþ 7 
 7 ¼ 40 
 7

3x¼ 33

3 x

3

¼

33

3

x¼$ 11

2x¼$ 22

Hence, the first server received $22, the second server received $11, and the

third server received $7.

Step 4 Check: $22þ$11þ$7¼$40

146 CHAPTER 7 Expression and Equations