Xandra, Yoko and Julie had a total of 98 buttons. The ratio of Yoko's buttons to Julie's buttons was at first 12 : 5. After Xandra and Yoko each gave half of their buttons away, the 3 children had 59 buttons left. How many buttons did Xandra and Julie have at first?
| |
Xandra |
Yoko |
Julie |
Total |
| Before |
2 p |
12 u |
5 u |
98 |
| Change |
- 1 p |
- 6 u |
|
- 39 |
| After |
1 p |
6 u |
5 u |
59 |
Number of buttons that Xandra and Yoko gave away
= 98 - 59
= 39
1 p + 6 u = 39
1 p = 39 - 6 u --- (1)
1 p + 6 u + 5 u = 59
1 p + 11 u = 59
1 p = 59 - 11 u --- (2)
(1) = (2)
39 - 6 u = 59 - 11 u
11 u - 6 u = 59 - 39
5 u = 20
1 u = 20 ÷ 5 = 4
From (1)
1 p = 39 - 6 u
1 p = 39 - 6 x 4
1 p = 39 - 24 = 15
Number of buttons that Xandra and Julie had at first
= 2 p + 5 u
= 2 x 15 + 5 x 4
= 30 + 20
= 50
Answer(s): 50
