Albert and Ethan shared some buttons in the ratio of 3 : 8. After both each gave away 36 buttons to their brother, the ratio of the number of buttons Albert had to the total number of buttons left was 1 : 5. How many buttons did the two boys have at first?

	Albert	Ethan	Difference
Before	3x3 = 9 u	8x3 = 24 u	5x3 = 15 u
Change	- 36	- 36
After	1x5 = 5 u	4x5 = 20 u	3x5 = 15 u

Number of buttons that Albert and Ethan each gave to their brother is the same.

The difference in the number of buttons at first and in the end between Albert and Ethan remains unchanged.  Make the difference in the number of buttons the same.  LCM of 5 and 3 is 15.

Number of buttons that Albert gave to their brother
= 9 u - 5 u
= 4 u

4 u = 36

1 u = 36 ÷ 4 = 9

Number of buttons that the two boys had at first
= 9 u + 24 u
= 33 u
= 33 x 9
= 297

Answer(s): 297