Ethan, Elijah and Vaidev have some stickers. The ratios of their stickers are as follows:

Ethan : (Ethan + Elijah + Vaidev) = 3 : 7
Elijah : (Ethan + Vaidev) = 1 : 3

Vaidev has 6 stickers more than Elijah. In the end, Vaidev gives away all he has to Elijah and Ethan so that both Elijah and Ethan end up with the same number of stickers, how many stickers has Ethan received from Vaidev?

Elijah	Vaidev	Ethan	Total
4x4		3x4	7x4
1x7	3x7		4x7
7 u	9 u	12 u	28 u

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

Number of stickers that Vaidev has more than Elijah
= 9 u - 7 u
= 2 u

2 u = 6

1 u = 6 ÷ 2 = 3

	Elijah	Vaidev	Ethan
Before	7 u	9 u	12 u
Change	+ 7 u	- 9 u	+ 2 u
After	14 u	0 u	14 u

Number of stickers that Ethan has received from Vaidev
= 14 u - 12 u 
= 2 u
= 2 x 3
= 6

Answer(s): 6