Seth and Ben shared some buttons in the ratio of 3 : 8. After both each gave away 28 buttons to their brother, the ratio of the number of buttons Seth had to the total number of buttons left was 1 : 6. How many buttons did the two boys have at first?

	Seth	Ben	Difference
Before	3x4 = 12 u	8x4 = 32 u	5x4 = 20 u
Change	- 28	- 28
After	1x5 = 5 u	5x5 = 25 u	4x5 = 20 u

Number of buttons that Seth and Ben each gave to their brother is the same.

The difference in the number of buttons at first and in the end between Seth and Ben remains unchanged.  Make the difference in the number of buttons the same.  LCM of 5 and 4 is 20.

Number of buttons that Seth gave to their brother
= 12 u - 5 u
= 7 u

7 u = 28

1 u = 28 ÷ 7 = 4

Number of buttons that the two boys had at first
= 12 u + 32 u
= 44 u
= 44 x 4
= 176

Answer(s): 176