Riordan, Brandon and Xavier have some buttons. The ratios of their buttons are as follows:

Riordan : (Riordan + Brandon + Xavier) = 1 : 3
Brandon : (Riordan + Xavier) = 1 : 3

Xavier has 6 buttons more than Brandon. In the end, Xavier gives away all he has to Brandon and Riordan so that both Brandon and Riordan end up with the same number of buttons, how many buttons has Riordan received from Xavier?

Brandon	Xavier	Riordan	Total
2x4		1x4	3x4
1x3	3x3		4x3
3 u	5 u	4 u	12 u

The total number of buttons is repeated.  Make the total number of buttons the same.  LCM of 3 and 4 is 12.

Number of buttons that Xavier has more than Brandon
= 5 u - 3 u
= 2 u

2 u = 6

1 u = 6 ÷ 2 = 3

	Brandon	Xavier	Riordan
Before	3 u	5 u	4 u
Change	+ 3 u	- 5 u	+ 2 u
After	6 u	0 u	6 u

Number of buttons that Riordan has received from Xavier
= 6 u - 4 u 
= 2 u
= 2 x 3
= 6

Answer(s): 6