Reggie, Valen and Jeremy have some buttons. The ratios of their buttons are as follows:

Reggie : (Reggie + Valen + Jeremy) = 1 : 3
Valen : (Reggie + Jeremy) = 1 : 5

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

Valen	Jeremy	Reggie	Total
2x2		1x2	3x2
1x1	5x1		6x1
1 u	3 u	2 u	6 u

The total number of buttons is repeated.  Make the total number of buttons the same.  LCM of 3 and 6 is 6.

Number of buttons that Jeremy has more than Valen
= 3 u - 1 u
= 2 u

2 u = 6

1 u = 6 ÷ 2 = 3

	Valen	Jeremy	Reggie
Before	1 u	3 u	2 u
Change	+ 2 u	- 3 u	+ 1 u
After	3 u	0 u	3 u

Number of buttons that Valen has received from Jeremy
= 3 u - 1 u 
= 2 u
= 2 x 3
= 6

Answer(s): 6