Howard, Warren and Luke had a total of 147 marbles. The ratio of the number of marbles that Warren had to the number of marbles that Luke had was 6 : 7. After Howard and Warren each gave away half of their marbles, the 3 children had 112 marbles left. How many marbles did Warren and Luke have at first?
| |
Howard |
Warren |
Luke |
Total |
| Before |
2 p |
6 u |
7 u |
147 |
| Change |
- 1 p |
- 3 u |
|
- 35 |
| After |
1 p |
3 u |
7 u |
112 |
Total number of marbles that Howard and Warren gave away
= 147 - 112
= 35
1 p + 3 u = 35 --- (1)
1 p + 3 u + 7 u = 112
1 p + 10 u = 112 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 3 u) = 112 - 35
10 u - 3 u = 77
7 u = 77
1 u = 77 ÷ 7 = 11
Total number of marbles that Warren and Luke had at first
= 6 u + 7 u
= 13 u
= 13 x 11
= 143
Answer(s): 143
