Howard, Jenson and Fred had a total of 158 stamps. The ratio of the number of stamps that Jenson had to the number of stamps that Fred had was 8 : 7. After Howard and Jenson each gave away half of their stamps, the 3 children had 114 stamps left. How many stamps did Jenson and Fred have at first?
| |
Howard |
Jenson |
Fred |
Total |
| Before |
2 p |
8 u |
7 u |
158 |
| Change |
- 1 p |
- 4 u |
|
- 44 |
| After |
1 p |
4 u |
7 u |
114 |
Total number of stamps that Howard and Jenson gave away
= 158 - 114
= 44
1 p + 4 u = 44 --- (1)
1 p + 4 u + 7 u = 114
1 p + 11 u = 114 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 4 u) = 114 - 44
11 u - 4 u = 70
7 u = 70
1 u = 70 ÷ 7 = 10
Total number of stamps that Jenson and Fred had at first
= 8 u + 7 u
= 15 u
= 15 x 10
= 150
Answer(s): 150
