Julian, Xavier and Reggie have some beads. The ratios of their beads are as follows:

Julian : (Julian + Xavier + Reggie) = 3 : 7
Xavier : (Julian + Reggie) = 1 : 3

Reggie has 24 beads more than Xavier. In the end, Reggie gives away all he has to Xavier and Julian so that both Xavier and Julian end up with the same number of beads, how many beads has Xavier received from Reggie?

Xavier	Reggie	Julian	Total
4x4		3x4	7x4
1x7	3x7		4x7
7 u	9 u	12 u	28 u

The total number of beads is repeated.  Make the total number of beads the same.  LCM of 7 and 4 is 28.

Number of beads that Reggie has more than Xavier
= 9 u - 7 u
= 2 u

2 u = 24

1 u = 24 ÷ 2 = 12

	Xavier	Reggie	Julian
Before	7 u	9 u	12 u
Change	+ 7 u	- 9 u	+ 2 u
After	14 u	0 u	14 u

Number of beads that Xavier has received from Reggie
= 14 u - 7 u 
= 7 u
= 7 x 12
= 84

Answer(s): 84