Min, Jane and Kylie had a total of 244 buttons. The ratio of Jane's buttons to Kylie's buttons was at first 12 : 5. After Min and Jane each gave half of their buttons away, the 3 children had 152 buttons left. How many buttons did Min and Kylie have at first?
| |
Min |
Jane |
Kylie |
Total |
| Before |
2 p |
12 u |
5 u |
244 |
| Change |
- 1 p |
- 6 u |
|
- 92 |
| After |
1 p |
6 u |
5 u |
152 |
Number of buttons that Min and Jane gave away
= 244 - 152
= 92
1 p + 6 u = 92
1 p = 92 - 6 u --- (1)
1 p + 6 u + 5 u = 152
1 p + 11 u = 152
1 p = 152 - 11 u --- (2)
(1) = (2)
92 - 6 u = 152 - 11 u
11 u - 6 u = 152 - 92
5 u = 60
1 u = 60 ÷ 5 = 12
From (1)
1 p = 92 - 6 u
1 p = 92 - 6 x 12
1 p = 92 - 72 = 20
Number of buttons that Min and Kylie had at first
= 2 p + 5 u
= 2 x 20 + 5 x 12
= 40 + 60
= 100
Answer(s): 100
