Howard and Jenson shared some buttons in the ratio of 4 : 7. After both each gave away 55 buttons to their sister, the ratio of the number of buttons Howard had to the total number of buttons left was 1 : 4. How many buttons did the two boys have in the end?

	Howard	Jenson	Difference
Before	4x2 = 8 u	7x2 = 14 u	3x2 = 6 u
Change	- 55	- 55
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of buttons that Howard and Jenson each gave to their sister is the same.

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

Number of buttons that Howard gave to their sister
= 8 u - 3 u
= 5 u

5 u = 55

1 u = 55 ÷ 5 = 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