Lee and Ivan shared some buttons in the ratio of 5 : 8. After both each gave away 24 buttons to their sister, the ratio of the number of buttons Lee had to the total number of buttons left was 1 : 3. How many buttons did the two boys have in the end?

	Lee	Ivan	Difference
Before	5x1 = 5 u	8x1 = 8 u	3x1 = 3 u
Change	- 24	- 24
After	1x3 = 3 u	2x3 = 6 u	1x3 = 3 u

Number of buttons that Lee and Ivan each gave to their sister is the same.

The difference in the number of buttons at first and in the end between Lee and Ivan remains unchanged.  Make the difference in the number of buttons the same.  LCM of 3 and 1 is 3.

Number of buttons that Lee gave to their sister
= 5 u - 3 u
= 2 u

2 u = 24

1 u = 24 ÷ 2 = 12

Number of buttons that the two boys had in the end
= 3 u + 6 u
= 9 u
= 9 x 12
= 108

Answer(s): 108