Luke, Julian and Carl have some beads. The ratios of their beads are as follows:
Luke : (Luke + Julian + Carl) = 1 : 3
Julian : (Luke + Carl) = 1 : 5
Carl has 14 beads more than Julian. In the end, Carl gives away all he has to Julian and Luke so that both Julian and Luke end up with the same number of beads, how many beads has Julian received from Carl?
Julian |
Carl |
Luke |
Total |
2x2 |
1x2 |
3x2 |
1x1 |
5x1 |
6x1 |
1 u |
3 u |
2 u |
6 u |
The total number of beads is repeated. Make the total number of beads the same. LCM of 3 and 6 is 6.
Number of beads that Carl has more than Julian
= 3 u - 1 u
= 2 u
2 u = 14
1 u = 14 ÷ 2 = 7
|
Julian |
Carl |
Luke |
Before |
1 u |
3 u |
2 u |
Change |
+ 2 u |
- 3 u |
+ 1 u |
After |
3 u |
0 u |
3 u |
Number of beads that Julian has received from Carl
= 3 u - 1 u
= 2 u
= 2 x 7
= 14
Answer(s): 14