John, Bryan and Ethan had a total of 100 stickers. The ratio of the number of stickers that Bryan had to the number of stickers that Ethan had was 4 : 7. After John and Bryan each gave away half of their stickers, the 3 children had 78 stickers left. How many stickers did Bryan and Ethan have in the end?
| |
John |
Bryan |
Ethan |
Total |
| Before |
2 p |
4 u |
7 u |
100 |
| Change |
- 1 p |
- 2 u |
|
- 22 |
| After |
1 p |
2 u |
7 u |
78 |
Total number of stickers that John and Bryan gave away
= 100 - 78
= 22
1 p + 2 u = 22 --- (1)
1 p + 2 u + 7 u = 78
1 p + 9 u = 78 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 78 - 22
9 u - 2 u = 56
7 u = 56
1 u = 56 ÷ 7 = 8
Total number of stickers that Bryan and Ethan had in the end
= 2 u + 7 u
= 9 u
= 9 x 8
= 72
Answer(s): 72
