Ian and Flynn shared some buttons in the ratio of 4 : 7. After both each gave away 10 buttons to their sister, the ratio of the number of buttons Ian had to the total number of buttons left was 1 : 4. How many buttons did the two boys have in the end?

	Ian	Flynn	Difference
Before	4x2 = 8 u	7x2 = 14 u	3x2 = 6 u
Change	- 10	- 10
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of buttons that Ian and Flynn each gave to their sister is the same.

The difference in the number of buttons at first and in the end between Ian and Flynn remains unchanged.  Make the difference in the number of buttons the same.  LCM of 3 and 2 is 6.

Number of buttons that Ian gave to their sister
= 8 u - 3 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

Number of buttons that the two boys had in the end
= 3 u + 9 u
= 12 u
= 12 x 2
= 24

Answer(s): 24