Bobby, Elijah and Wesley had a total of 87 marbles. The ratio of the number of marbles that Elijah had to the number of marbles that Wesley had was 4 : 5. After Bobby and Elijah each gave away half of their marbles, the 3 children had 61 marbles left. How many marbles did Elijah and Wesley have at first?
| |
Bobby |
Elijah |
Wesley |
Total |
| Before |
2 p |
4 u |
5 u |
87 |
| Change |
- 1 p |
- 2 u |
|
- 26 |
| After |
1 p |
2 u |
5 u |
61 |
Total number of marbles that Bobby and Elijah gave away
= 87 - 61
= 26
1 p + 2 u = 26 --- (1)
1 p + 2 u + 5 u = 61
1 p + 7 u = 61 --- (2)
(2) - (1)
(1 p + 7 u) - (1 p + 2 u) = 61 - 26
7 u - 2 u = 35
5 u = 35
1 u = 35 ÷ 5 = 7
Total number of marbles that Elijah and Wesley had at first
= 4 u + 5 u
= 9 u
= 9 x 7
= 63
Answer(s): 63
