STRATEGY: Letx¼the smaller number and xþ 8 ¼the larger number.
Since the problem asked for the sum, write the equation asxþxþ 8 ¼26.
IMPLEMENTATION: Solve the equation forx:
xþxþ 8 ¼ 26
2 xþ 8 ¼ 26
2 xþ 8 8 ¼ 26 8
2 x¼ 18
21 x
21
¼
18
2
x¼ 9
Hence one number is 9 and the other number isxþ8or9þ 8 ¼17.
EVALUATION: Check the answer: 9þ 17 ¼ 26
EXAMPLE:If eight plus three times a number is equal to 23, find the
number.
SOLUTION:
GOAL: You are being asked to find one number.
STRATEGY: Letx¼the number. Eight plus three times a number is written
as 8þ 3 xand the equation is 8þ 3 x¼23.
IMPLEMENTATION: Solve the equation.
8 þ 3 x¼ 23
8 8 þ 3 x¼ 23 8
3 x¼ 15
31 x
31
¼
15
3
x¼ 5
LESSON 9 Solving Number Problems 89