Billy and Michael had some marbles in the ratio of 5 : 4. Michael and Julian had some marbles in the ratio of 2 : 1. Billy sold 9 marbles to Julian and ended up with half the number of marbles Michael had. How many marbles did Julian have in the end?
| Billy |
Michael |
Julian |
| 5x1 |
4x1 |
|
| |
2x2 |
1x2 |
| 5 u |
4 u |
2 u |
The number of marbles that Michael had at first is repeated. Make the number of marbles that Michael had at first the same. LCM of 4 and 2 is 4.
| |
Billy |
Michael |
Julian |
| Before |
5 u |
4 u |
2 u |
| Change |
- 9 |
|
+ 9 |
| After |
2 u |
4 u |
2 u + 9 |
Number of marbles that Billy had in the end
= 4 u ÷ 2
= 2 u
Number of marbles that Billy sold to Julian
= 5 u - 2 u
= 3 u
3 u = 9
1 u = 9 ÷ 3 = 3
Number of marbles that Julian had in the end
= 2 u + 9
= 2 x 3 + 9
= 6 + 9
= 15
Answer(s): 15
