Ivan, Jack and Oliver had a total of 110 buttons. The ratio of the number of buttons that Jack had to the number of buttons that Oliver had was 8 : 7. After Ivan and Jack each gave away half of their buttons, the 3 children had 76 buttons left. How many buttons did Jack and Oliver have at first?
| |
Ivan |
Jack |
Oliver |
Total |
| Before |
2 p |
8 u |
7 u |
110 |
| Change |
- 1 p |
- 4 u |
|
- 34 |
| After |
1 p |
4 u |
7 u |
76 |
Total number of buttons that Ivan and Jack gave away
= 110 - 76
= 34
1 p + 4 u = 34 --- (1)
1 p + 4 u + 7 u = 76
1 p + 11 u = 76 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 4 u) = 76 - 34
11 u - 4 u = 42
7 u = 42
1 u = 42 ÷ 7 = 6
Total number of buttons that Jack and Oliver had at first
= 8 u + 7 u
= 15 u
= 15 x 6
= 90
Answer(s): 90
