Julian, Luis and Bobby had a total of 126 marbles. The ratio of the number of marbles that Luis had to the number of marbles that Bobby had was 8 : 5. After Julian and Luis each gave away half of their marbles, the 3 children had 83 marbles left. How many marbles did Luis and Bobby have in the end?
| |
Julian |
Luis |
Bobby |
Total |
| Before |
2 p |
8 u |
5 u |
126 |
| Change |
- 1 p |
- 4 u |
|
- 43 |
| After |
1 p |
4 u |
5 u |
83 |
Total number of marbles that Julian and Luis gave away
= 126 - 83
= 43
1 p + 4 u = 43 --- (1)
1 p + 4 u + 5 u = 83
1 p + 9 u = 83 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 4 u) = 83 - 43
9 u - 4 u = 40
5 u = 40
1 u = 40 ÷ 5 = 8
Total number of marbles that Luis and Bobby had in the end
= 4 u + 5 u
= 9 u
= 9 x 8
= 72
Answer(s): 72
