Justin and Julian shared some buttons in the ratio of 5 : 7. After both each gave away 26 buttons to their sister, the ratio of the number of buttons Justin had to the total number of buttons left was 1 : 5. How many buttons did the two boys have in the end?

	Justin	Julian	Difference
Before	5x3 = 15 u	7x3 = 21 u	2x3 = 6 u
Change	- 26	- 26
After	1x2 = 2 u	4x2 = 8 u	3x2 = 6 u

Number of buttons that Justin and Julian each gave to their sister is the same.

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

Number of buttons that Justin gave to their sister
= 15 u - 2 u
= 13 u

13 u = 26

1 u = 26 ÷ 13 = 2

Number of buttons that the two boys had in the end
= 2 u + 8 u
= 10 u
= 10 x 2
= 20

Answer(s): 20