Andy, Harry and George had a total of 43 buttons. The ratio of the number of buttons that Harry had to the number of buttons that George had was 4 : 7. After Andy and Harry each gave away half of their buttons, the 3 children had 32 buttons left. How many buttons did Harry and George have in the end?
| |
Andy |
Harry |
George |
Total |
| Before |
2 p |
4 u |
7 u |
43 |
| Change |
- 1 p |
- 2 u |
|
- 11 |
| After |
1 p |
2 u |
7 u |
32 |
Total number of buttons that Andy and Harry gave away
= 43 - 32
= 11
1 p + 2 u = 11 --- (1)
1 p + 2 u + 7 u = 32
1 p + 9 u = 32 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 32 - 11
9 u - 2 u = 21
7 u = 21
1 u = 21 ÷ 7 = 3
Total number of buttons that Harry and George had in the end
= 2 u + 7 u
= 9 u
= 9 x 3
= 27
Answer(s): 27
