Henry, Charlie and Jeremy have some buttons. The ratios of their buttons are as follows:

Henry : (Henry + Charlie + Jeremy) = 2 : 5
Charlie : (Henry + Jeremy) = 1 : 3

Jeremy has 18 buttons more than Charlie. In the end, Jeremy gives away all he has to Charlie and Henry so that both Charlie and Henry end up with the same number of buttons, how many buttons has Henry received from Jeremy?

Charlie	Jeremy	Henry	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 Jeremy has more than Charlie
= 7 u - 5 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

	Charlie	Jeremy	Henry
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 Henry has received from Jeremy
= 10 u - 8 u 
= 2 u
= 2 x 9
= 18

Answer(s): 18