Nick and David shared some buttons in the ratio of 5 : 7. After both each gave away 39 buttons to their sister, the ratio of the number of buttons Nick had to the total number of buttons left was 1 : 5. How many buttons did the two boys have in the end?

	Nick	David	Difference
Before	5x3 = 15 u	7x3 = 21 u	2x3 = 6 u
Change	- 39	- 39
After	1x2 = 2 u	4x2 = 8 u	3x2 = 6 u

Number of buttons that Nick and David each gave to their sister is the same.

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

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

13 u = 39

1 u = 39 ÷ 13 = 3

Number of buttons that the two boys had in the end
= 2 u + 8 u
= 10 u
= 10 x 3
= 30

Answer(s): 30