Neave and Bryan shared some buttons in the ratio of 4 : 7. After both each gave away 91 buttons to their sister, the ratio of the number of buttons Neave had to the total number of buttons left was 1 : 6. How many buttons did the two boys have in the end?

	Neave	Bryan	Difference
Before	4x4 = 16 u	7x4 = 28 u	3x4 = 12 u
Change	- 91	- 91
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of buttons that Neave and Bryan each gave to their sister is the same.

The difference in the number of buttons at first and in the end between Neave and Bryan remains unchanged.  Make the difference in the number of buttons the same.  LCM of 3 and 4 is 12.

Number of buttons that Neave gave to their sister
= 16 u - 3 u
= 13 u

13 u = 91

1 u = 91 ÷ 13 = 7

Number of buttons that the two boys had in the end
= 3 u + 15 u
= 18 u
= 18 x 7
= 126

Answer(s): 126