Gem, Shannon and Julie had a total of 129 buttons. The ratio of Shannon's buttons to Julie's buttons was at first 12 : 7. After Gem and Shannon each gave half of their buttons away, the 3 children had 82 buttons left. How many buttons did Gem and Julie have at first?
| |
Gem |
Shannon |
Julie |
Total |
| Before |
2 p |
12 u |
7 u |
129 |
| Change |
- 1 p |
- 6 u |
|
- 47 |
| After |
1 p |
6 u |
7 u |
82 |
Number of buttons that Gem and Shannon gave away
= 129 - 82
= 47
1 p + 6 u = 47
1 p = 47 - 6 u --- (1)
1 p + 6 u + 7 u = 82
1 p + 13 u = 82
1 p = 82 - 13 u --- (2)
(1) = (2)
47 - 6 u = 82 - 13 u
13 u - 6 u = 82 - 47
7 u = 35
1 u = 35 ÷ 7 = 5
From (1)
1 p = 47 - 6 u
1 p = 47 - 6 x 5
1 p = 47 - 30 = 17
Number of buttons that Gem and Julie had at first
= 2 p + 7 u
= 2 x 17 + 7 x 5
= 34 + 35
= 69
Answer(s): 69
