Jade, Zara and Shiyun had a total of 125 buttons. The ratio of Zara's buttons to Shiyun's buttons was at first 4 : 7. After Jade and Zara each gave half of their buttons away, the 3 children had 87 buttons left. How many buttons did Jade and Shiyun have at first?
| |
Jade |
Zara |
Shiyun |
Total |
| Before |
2 p |
4 u |
7 u |
125 |
| Change |
- 1 p |
- 2 u |
|
- 38 |
| After |
1 p |
2 u |
7 u |
87 |
Number of buttons that Jade and Zara gave away
= 125 - 87
= 38
1 p + 2 u = 38
1 p = 38 - 2 u --- (1)
1 p + 2 u + 7 u = 87
1 p + 9 u = 87
1 p = 87 - 9 u --- (2)
(1) = (2)
38 - 2 u = 87 - 9 u
9 u - 2 u = 87 - 38
7 u = 49
1 u = 49 ÷ 7 = 7
From (1)
1 p = 38 - 2 u
1 p = 38 - 2 x 7
1 p = 38 - 14 = 24
Number of buttons that Jade and Shiyun had at first
= 2 p + 7 u
= 2 x 24 + 7 x 7
= 48 + 49
= 97
Answer(s): 97
