Ivan, Jeremy and Perry had a total of 96 marbles. The ratio of the number of marbles that Jeremy had to the number of marbles that Perry had was 2 : 9. After Ivan and Jeremy each gave away half of their marbles, the 3 children had 84 marbles left. How many marbles did Jeremy and Perry have at first?
| |
Ivan |
Jeremy |
Perry |
Total |
| Before |
2 p |
2 u |
9 u |
96 |
| Change |
- 1 p |
- 1 u |
|
- 12 |
| After |
1 p |
1 u |
9 u |
84 |
Total number of marbles that Ivan and Jeremy gave away
= 96 - 84
= 12
1 p + 1 u = 12 --- (1)
1 p + 1 u + 9 u = 84
1 p + 10 u = 84 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 1 u) = 84 - 12
10 u - 1 u = 72
9 u = 72
1 u = 72 ÷ 9 = 8
Total number of marbles that Jeremy and Perry had at first
= 2 u + 9 u
= 11 u
= 11 x 8
= 88
Answer(s): 88
