Billy, Ethan and David have some buttons. The ratios of their buttons are as follows:

Billy : (Billy + Ethan + David) = 2 : 5
Ethan : (Billy + David) = 1 : 5

David has 96 buttons more than Ethan. In the end, David gives away all he has to Ethan and Billy so that both Ethan and Billy end up with the same number of buttons, how many buttons has Billy received from David?

Ethan	David	Billy	Total
3x6		2x6	5x6
1x5	5x5		6x5
5 u	13 u	12 u	30 u

The total number of buttons is repeated.  Make the total number of buttons the same.  LCM of 5 and 6 is 30.

Number of buttons that David has more than Ethan
= 13 u - 5 u
= 8 u

8 u = 96

1 u = 96 ÷ 8 = 12

	Ethan	David	Billy
Before	5 u	13 u	12 u
Change	+ 10 u	- 13 u	+ 3 u
After	15 u	0 u	15 u

Number of buttons that Billy has received from David
= 15 u - 12 u 
= 3 u
= 3 x 12
= 36

Answer(s): 36