Luke, Billy and George have some marbles. The ratios of their marbles are as follows:

Luke : (Luke + Billy + George) = 1 : 4
Billy : (Luke + George) = 1 : 5

George has 60 marbles more than Billy. In the end, George gives away all he has to Billy and Luke so that both Billy and Luke end up with the same number of marbles, how many marbles has Billy received from George?

Billy	George	Luke	Total
3x3		1x3	4x3
1x2	5x2		6x2
2 u	7 u	3 u	12 u

The total number of marbles is repeated.  Make the total number of marbles the same.  LCM of 4 and 6 is 12.

Number of marbles that George has more than Billy
= 7 u - 2 u
= 5 u

5 u = 60

1 u = 60 ÷ 5 = 12

	Billy	George	Luke
Before	2 u	7 u	3 u
Change	+ 4 u	- 7 u	+ 3 u
After	6 u	0 u	6 u

Number of marbles that Billy has received from George
= 6 u - 2 u 
= 4 u
= 4 x 12
= 48

Answer(s): 48