Mark, Gabriel and Howard had a total of 24 stamps. The ratio of the number of stamps that Gabriel had to the number of stamps that Howard had was 2 : 7. After Mark and Gabriel each gave away half of their stamps, the 3 children had 19 stamps left. How many stamps did Gabriel and Howard have at first?
| |
Mark |
Gabriel |
Howard |
Total |
| Before |
2 p |
2 u |
7 u |
24 |
| Change |
- 1 p |
- 1 u |
|
- 5 |
| After |
1 p |
1 u |
7 u |
19 |
Total number of stamps that Mark and Gabriel gave away
= 24 - 19
= 5
1 p + 1 u = 5 --- (1)
1 p + 1 u + 7 u = 19
1 p + 8 u = 19 --- (2)
(2) - (1)
(1 p + 8 u) - (1 p + 1 u) = 19 - 5
8 u - 1 u = 14
7 u = 14
1 u = 14 ÷ 7 = 2
Total number of stamps that Gabriel and Howard had at first
= 2 u + 7 u
= 9 u
= 9 x 2
= 18
Answer(s): 18
