Oliver, Jeremy and Pierre had a total of 51 buttons. The ratio of the number of buttons that Jeremy had to the number of buttons that Pierre had was 2 : 5. After Oliver and Jeremy each gave away half of their buttons, the 3 children had 38 buttons left. How many buttons did Jeremy and Pierre have at first?
| |
Oliver |
Jeremy |
Pierre |
Total |
| Before |
2 p |
2 u |
5 u |
51 |
| Change |
- 1 p |
- 1 u |
|
- 13 |
| After |
1 p |
1 u |
5 u |
38 |
Total number of buttons that Oliver and Jeremy gave away
= 51 - 38
= 13
1 p + 1 u = 13 --- (1)
1 p + 1 u + 5 u = 38
1 p + 6 u = 38 --- (2)
(2) - (1)
(1 p + 6 u) - (1 p + 1 u) = 38 - 13
6 u - 1 u = 25
5 u = 25
1 u = 25 ÷ 5 = 5
Total number of buttons that Jeremy and Pierre had at first
= 2 u + 5 u
= 7 u
= 7 x 5
= 35
Answer(s): 35
