Paul, Asher and Billy had a total of 67 buttons. The ratio of the number of buttons that Asher had to the number of buttons that Billy had was 4 : 7. After Paul and Asher each gave away half of their buttons, the 3 children had 51 buttons left. How many buttons did Asher and Billy have at first?
| |
Paul |
Asher |
Billy |
Total |
| Before |
2 p |
4 u |
7 u |
67 |
| Change |
- 1 p |
- 2 u |
|
- 16 |
| After |
1 p |
2 u |
7 u |
51 |
Total number of buttons that Paul and Asher gave away
= 67 - 51
= 16
1 p + 2 u = 16 --- (1)
1 p + 2 u + 7 u = 51
1 p + 9 u = 51 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 51 - 16
9 u - 2 u = 35
7 u = 35
1 u = 35 ÷ 7 = 5
Total number of buttons that Asher and Billy had at first
= 4 u + 7 u
= 11 u
= 11 x 5
= 55
Answer(s): 55
