Fred, Albert and Howard have some buttons. The ratios of their buttons are as follows:

Fred : (Fred + Albert + Howard) = 1 : 5
Albert : (Fred + Howard) = 1 : 5

Howard has 112 buttons more than Albert. In the end, Howard gives away all he has to Albert and Fred so that both Albert and Fred end up with the same number of buttons, how many buttons has Fred received from Howard?

Albert	Howard	Fred	Total
4x6		1x6	5x6
1x5	5x5		6x5
5 u	19 u	6 u	30 u

The total number of buttons is repeated.  Make the total number of buttons the same.  LCM of 5 and 6 is 30.

Number of buttons that Howard has more than Albert
= 19 u - 5 u
= 14 u

14 u = 112

1 u = 112 ÷ 14 = 8

	Albert	Howard	Fred
Before	5 u	19 u	6 u
Change	+ 10 u	- 19 u	+ 9 u
After	15 u	0 u	15 u

Number of buttons that Fred has received from Howard
= 15 u - 6 u 
= 9 u
= 9 x 8
= 72

Answer(s): 72