David and Luke had some marbles in the ratio of 7 : 5. Luke and Will had some marbles in the ratio of 2 : 1. David sold 99 marbles to Will and ended up with half the number of marbles Luke had. How many marbles did Will have in the end?
| David |
Luke |
Will |
| 7x2 |
5x2 |
|
| |
2x5 |
1x5 |
| 14 u |
10 u |
5 u |
The number of marbles that Luke had at first is repeated. Make the number of marbles that Luke had at first the same. LCM of 5 and 2 is 10.
| |
David |
Luke |
Will |
| Before |
14 u |
10 u |
5 u |
| Change |
- 99 |
|
+ 99 |
| After |
5 u |
10 u |
5 u + 99 |
Number of marbles that David had in the end
= 10 u ÷ 2
= 5 u
Number of marbles that David sold to Will
= 14 u - 5 u
= 9 u
9 u = 99
1 u = 99 ÷ 9 = 11
Number of marbles that Will had in the end
= 5 u + 99
= 5 x 11 + 99
= 55 + 99
= 154
Answer(s): 154
