Jeremy, Daniel and Xavier have some buttons. The ratios of their buttons are as follows:

Jeremy : (Jeremy + Daniel + Xavier) = 2 : 5
Daniel : (Jeremy + Xavier) = 1 : 3

Xavier has 14 buttons more than Daniel. In the end, Xavier gives away all he has to Daniel and Jeremy so that both Daniel and Jeremy end up with the same number of buttons, how many buttons has Jeremy received from Xavier?

Daniel	Xavier	Jeremy	Total
3x4		2x4	5x4
1x5	3x5		4x5
5 u	7 u	8 u	20 u

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

Number of buttons that Xavier has more than Daniel
= 7 u - 5 u
= 2 u

2 u = 14

1 u = 14 ÷ 2 = 7

	Daniel	Xavier	Jeremy
Before	5 u	7 u	8 u
Change	+ 5 u	- 7 u	+ 2 u
After	10 u	0 u	10 u

Number of buttons that Jeremy has received from Xavier
= 10 u - 8 u 
= 2 u
= 2 x 7
= 14

Answer(s): 14