Howard and Charlie shared some buttons in the ratio of 3 : 7. After both each gave away 40 buttons to their cousin, the ratio of the number of buttons Howard had to the total number of buttons left was 1 : 5. How many buttons did the two boys have at first?

	Howard	Charlie	Difference
Before	3x3 = 9 u	7x3 = 21 u	4x3 = 12 u
Change	- 40	- 40
After	1x4 = 4 u	4x4 = 16 u	3x4 = 12 u

Number of buttons that Howard and Charlie each gave to their cousin is the same.

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

Number of buttons that Howard gave to their cousin
= 9 u - 4 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

Number of buttons that the two boys had at first
= 9 u + 21 u
= 30 u
= 30 x 8
= 240

Answer(s): 240