Luke and Perry shared some buttons in the ratio of 3 : 8. After both each gave away 20 buttons to their brother, the ratio of the number of buttons Luke had to the total number of buttons left was 1 : 5. How many buttons did the two boys have in the end?

	Luke	Perry	Difference
Before	3x3 = 9 u	8x3 = 24 u	5x3 = 15 u
Change	- 20	- 20
After	1x5 = 5 u	4x5 = 20 u	3x5 = 15 u

Number of buttons that Luke and Perry each gave to their brother is the same.

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

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

4 u = 20

1 u = 20 ÷ 4 = 5

Number of buttons that the two boys had in the end
= 5 u + 20 u
= 25 u
= 25 x 5
= 125

Answer(s): 125