Jeremy and Ken shared some buttons in the ratio of 5 : 8. After both each gave away 77 buttons to their brother, the ratio of the number of buttons Jeremy had to the total number of buttons left was 1 : 4. How many buttons did the two boys have in the end?

	Jeremy	Ken	Difference
Before	5x2 = 10 u	8x2 = 16 u	3x2 = 6 u
Change	- 77	- 77
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of buttons that Jeremy and Ken each gave to their brother is the same.

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

Number of buttons that Jeremy gave to their brother
= 10 u - 3 u
= 7 u

7 u = 77

1 u = 77 ÷ 7 = 11

Number of buttons that the two boys had in the end
= 3 u + 9 u
= 12 u
= 12 x 11
= 132

Answer(s): 132