Xuan, Gwen and Erika had a total of 204 stickers. The ratio of Gwen's stickers to Erika's stickers was at first 8 : 5. After Xuan and Gwen each gave half of their stickers away, the 3 children had 132 stickers left. How many stickers did Xuan and Erika have at first?
| |
Xuan |
Gwen |
Erika |
Total |
| Before |
2 p |
8 u |
5 u |
204 |
| Change |
- 1 p |
- 4 u |
|
- 72 |
| After |
1 p |
4 u |
5 u |
132 |
Number of stickers that Xuan and Gwen gave away
= 204 - 132
= 72
1 p + 4 u = 72
1 p = 72 - 4 u --- (1)
1 p + 4 u + 5 u = 132
1 p + 9 u = 132
1 p = 132 - 9 u --- (2)
(1) = (2)
72 - 4 u = 132 - 9 u
9 u - 4 u = 132 - 72
5 u = 60
1 u = 60 ÷ 5 = 12
From (1)
1 p = 72 - 4 u
1 p = 72 - 4 x 12
1 p = 72 - 48 = 24
Number of stickers that Xuan and Erika had at first
= 2 p + 5 u
= 2 x 24 + 5 x 12
= 48 + 60
= 108
Answer(s): 108
