Wesley, David and Charlie had a total of 28 buttons. The ratio of the number of buttons that David had to the number of buttons that Charlie had was 2 : 3. After Wesley and David each gave away half of their buttons, the 3 children had 17 buttons left. How many buttons did David and Charlie have at first?
| |
Wesley |
David |
Charlie |
Total |
| Before |
2 p |
2 u |
3 u |
28 |
| Change |
- 1 p |
- 1 u |
|
- 11 |
| After |
1 p |
1 u |
3 u |
17 |
Total number of buttons that Wesley and David gave away
= 28 - 17
= 11
1 p + 1 u = 11 --- (1)
1 p + 1 u + 3 u = 17
1 p + 4 u = 17 --- (2)
(2) - (1)
(1 p + 4 u) - (1 p + 1 u) = 17 - 11
4 u - 1 u = 6
3 u = 6
1 u = 6 ÷ 3 = 2
Total number of buttons that David and Charlie had at first
= 2 u + 3 u
= 5 u
= 5 x 2
= 10
Answer(s): 10
