Simon, Oliver and Zane have some buttons. The ratios of their buttons are as follows:

Simon : (Simon + Oliver + Zane) = 3 : 7
Oliver : (Simon + Zane) = 1 : 3

Zane has 20 buttons more than Oliver. In the end, Zane gives away all he has to Oliver and Simon so that both Oliver and Simon end up with the same number of buttons, how many buttons has Simon received from Zane?

Oliver	Zane	Simon	Total
4x4		3x4	7x4
1x7	3x7		4x7
7 u	9 u	12 u	28 u

The total number of buttons is repeated.  Make the total number of buttons the same.  LCM of 7 and 4 is 28.

Number of buttons that Zane has more than Oliver
= 9 u - 7 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

	Oliver	Zane	Simon
Before	7 u	9 u	12 u
Change	+ 7 u	- 9 u	+ 2 u
After	14 u	0 u	14 u

Number of buttons that Simon has received from Zane
= 14 u - 12 u 
= 2 u
= 2 x 10
= 20

Answer(s): 20