Winnie, Xylia and Barbara had a total of 121 coins. The ratio of Xylia's coins to Barbara's coins was at first 8 : 7. After Winnie and Xylia each gave half of their coins away, the 3 children had 78 coins left. How many coins did Winnie and Xylia have at first?
| |
Winnie |
Xylia |
Barbara |
Total |
| Before |
2 p |
8 u |
7 u |
121 |
| Change |
- 1 p |
- 4 u |
|
- 43 |
| After |
1 p |
4 u |
7 u |
78 |
Number of coins that Winnie and Xylia gave away
= 121 - 78
= 43
1 p + 4 u = 43
1 p = 43 - 4 u --- (1)
1 p + 4 u + 7 u = 78
1 p + 11 u = 78
1 p = 78 - 11 u --- (2)
(1) = (2)
43 - 4 u = 78 - 11 u
11 u - 4 u = 78 - 43
7 u = 35
1 u = 35 ÷ 7 = 5
From (1)
1 p = 43 - 4 u
1 p = 43 - 4 x 5
1 p = 43 - 20 = 23
Number of coins that Winnie and Xylia had at first
= 2 p + 8 u
= 2 x 23 + 8 x 5
= 46 + 35
= 81
Answer(s): 81
