Seth, Michael and Julian have some buttons. The ratios of their buttons are as follows:

Seth : (Seth + Michael + Julian) = 1 : 4
Michael : (Seth + Julian) = 1 : 4

Julian has 28 buttons more than Michael. In the end, Julian gives away all he has to Michael and Seth so that both Michael and Seth end up with the same number of buttons, how many buttons has Michael received from Julian?

Michael	Julian	Seth	Total
3x5		1x5	4x5
1x4	4x4		5x4
4 u	11 u	5 u	20 u

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

Number of buttons that Julian has more than Michael
= 11 u - 4 u
= 7 u

7 u = 28

1 u = 28 ÷ 7 = 4

	Michael	Julian	Seth
Before	4 u	11 u	5 u
Change	+ 6 u	- 11 u	+ 5 u
After	10 u	0 u	10 u

Number of buttons that Michael has received from Julian
= 10 u - 4 u 
= 6 u
= 6 x 4
= 24

Answer(s): 24