George, Xavier and Archie have some beads. The ratios of their beads are as follows:

George : (George + Xavier + Archie) = 1 : 4
Xavier : (George + Archie) = 1 : 4

Archie has 21 beads more than Xavier. In the end, Archie gives away all he has to Xavier and George so that both Xavier and George end up with the same number of beads, how many beads has Xavier received from Archie?

Xavier	Archie	George	Total
3x5		1x5	4x5
1x4	4x4		5x4
4 u	11 u	5 u	20 u

The total number of beads is repeated.  Make the total number of beads the same.  LCM of 4 and 5 is 20.

Number of beads that Archie has more than Xavier
= 11 u - 4 u
= 7 u

7 u = 21

1 u = 21 ÷ 7 = 3

	Xavier	Archie	George
Before	4 u	11 u	5 u
Change	+ 6 u	- 11 u	+ 5 u
After	10 u	0 u	10 u

Number of beads that Xavier has received from Archie
= 10 u - 4 u 
= 6 u
= 6 x 3
= 18

Answer(s): 18