Sam, Lee and Fabian had a total of 137 marbles. The ratio of the number of marbles that Lee had to the number of marbles that Fabian had was 4 : 7. After Sam and Lee each gave away half of their marbles, the 3 children had 107 marbles left. How many marbles did Lee and Fabian have at first?
| |
Sam |
Lee |
Fabian |
Total |
| Before |
2 p |
4 u |
7 u |
137 |
| Change |
- 1 p |
- 2 u |
|
- 30 |
| After |
1 p |
2 u |
7 u |
107 |
Total number of marbles that Sam and Lee gave away
= 137 - 107
= 30
1 p + 2 u = 30 --- (1)
1 p + 2 u + 7 u = 107
1 p + 9 u = 107 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 107 - 30
9 u - 2 u = 77
7 u = 77
1 u = 77 ÷ 7 = 11
Total number of marbles that Lee and Fabian had at first
= 4 u + 7 u
= 11 u
= 11 x 11
= 121
Answer(s): 121
