Gabby, Olivia and Gem had a total of 65 buttons. The ratio of Olivia's buttons to Gem's buttons was at first 4 : 3. After Gabby and Olivia each gave half of their buttons away, the 3 children had 37 buttons left. How many buttons did Gabby and Gem have at first?
| |
Gabby |
Olivia |
Gem |
Total |
| Before |
2 p |
4 u |
3 u |
65 |
| Change |
- 1 p |
- 2 u |
|
- 28 |
| After |
1 p |
2 u |
3 u |
37 |
Number of buttons that Gabby and Olivia gave away
= 65 - 37
= 28
1 p + 2 u = 28
1 p = 28 - 2 u --- (1)
1 p + 2 u + 3 u = 37
1 p + 5 u = 37
1 p = 37 - 5 u --- (2)
(1) = (2)
28 - 2 u = 37 - 5 u
5 u - 2 u = 37 - 28
3 u = 9
1 u = 9 ÷ 3 = 3
From (1)
1 p = 28 - 2 u
1 p = 28 - 2 x 3
1 p = 28 - 6 = 22
Number of buttons that Gabby and Gem had at first
= 2 p + 3 u
= 2 x 22 + 3 x 3
= 44 + 9
= 53
Answer(s): 53
