Shiyun, Kathy and Linda had a total of 86 buttons. The ratio of Kathy's buttons to Linda's buttons was at first 6 : 7. After Shiyun and Kathy each gave half of their buttons away, the 3 children had 57 buttons left. How many buttons did Shiyun and Linda have at first?
| |
Shiyun |
Kathy |
Linda |
Total |
| Before |
2 p |
6 u |
7 u |
86 |
| Change |
- 1 p |
- 3 u |
|
- 29 |
| After |
1 p |
3 u |
7 u |
57 |
Number of buttons that Shiyun and Kathy gave away
= 86 - 57
= 29
1 p + 3 u = 29
1 p = 29 - 3 u --- (1)
1 p + 3 u + 7 u = 57
1 p + 10 u = 57
1 p = 57 - 10 u --- (2)
(1) = (2)
29 - 3 u = 57 - 10 u
10 u - 3 u = 57 - 29
7 u = 28
1 u = 28 ÷ 7 = 4
From (1)
1 p = 29 - 3 u
1 p = 29 - 3 x 4
1 p = 29 - 12 = 17
Number of buttons that Shiyun and Linda had at first
= 2 p + 7 u
= 2 x 17 + 7 x 4
= 34 + 28
= 62
Answer(s): 62
