Ethan, Pierre and Bryan have some buttons. The ratios of their buttons are as follows:

Ethan : (Ethan + Pierre + Bryan) = 1 : 4
Pierre : (Ethan + Bryan) = 1 : 5

Bryan has 35 buttons more than Pierre. In the end, Bryan gives away all he has to Pierre and Ethan so that both Pierre and Ethan end up with the same number of buttons, how many buttons has Ethan received from Bryan?

Pierre	Bryan	Ethan	Total
3x3		1x3	4x3
1x2	5x2		6x2
2 u	7 u	3 u	12 u

The total number of buttons is repeated.  Make the total number of buttons the same.  LCM of 4 and 6 is 12.

Number of buttons that Bryan has more than Pierre
= 7 u - 2 u
= 5 u

5 u = 35

1 u = 35 ÷ 5 = 7

	Pierre	Bryan	Ethan
Before	2 u	7 u	3 u
Change	+ 4 u	- 7 u	+ 3 u
After	6 u	0 u	6 u

Number of buttons that Ethan has received from Bryan
= 6 u - 3 u 
= 3 u
= 3 x 7
= 21

Answer(s): 21