Sam, Reggie and George have some buttons. The ratios of their buttons are as follows:

Sam : (Sam + Reggie + George) = 1 : 4
Reggie : (Sam + George) = 1 : 4

George has 49 buttons more than Reggie. In the end, George gives away all he has to Reggie and Sam so that both Reggie and Sam end up with the same number of buttons, how many buttons has Reggie received from George?

Reggie	George	Sam	Total
3x5		1x5	4x5
1x4	4x4		5x4
4 u	11 u	5 u	20 u

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

Number of buttons that George has more than Reggie
= 11 u - 4 u
= 7 u

7 u = 49

1 u = 49 ÷ 7 = 7

	Reggie	George	Sam
Before	4 u	11 u	5 u
Change	+ 6 u	- 11 u	+ 5 u
After	10 u	0 u	10 u

Number of buttons that Reggie has received from George
= 10 u - 4 u 
= 6 u
= 6 x 7
= 42

Answer(s): 42