John and Will shared some buttons in the ratio of 5 : 7. After both each gave away 65 buttons to their sister, the ratio of the number of buttons John had to the total number of buttons left was 1 : 5. How many buttons did the two boys have at first?

	John	Will	Difference
Before	5x3 = 15 u	7x3 = 21 u	2x3 = 6 u
Change	- 65	- 65
After	1x2 = 2 u	4x2 = 8 u	3x2 = 6 u

Number of buttons that John and Will each gave to their sister is the same.

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

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

13 u = 65

1 u = 65 ÷ 13 = 5

Number of buttons that the two boys had at first
= 15 u + 21 u
= 36 u
= 36 x 5
= 180

Answer(s): 180