Reggie and Ethan shared some stamps in the ratio of 4 : 7. After both each gave away 104 stamps to their sister, the ratio of the number of stamps Reggie had to the total number of stamps left was 1 : 6. How many stamps did the two boys have in the end?

	Reggie	Ethan	Difference
Before	4x4 = 16 u	7x4 = 28 u	3x4 = 12 u
Change	- 104	- 104
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of stamps that Reggie and Ethan each gave to their sister is the same.

The difference in the number of stamps at first and in the end between Reggie and Ethan remains unchanged.  Make the difference in the number of stamps the same.  LCM of 3 and 4 is 12.

Number of stamps that Reggie gave to their sister
= 16 u - 3 u
= 13 u

13 u = 104

1 u = 104 ÷ 13 = 8

Number of stamps that the two boys had in the end
= 3 u + 15 u
= 18 u
= 18 x 8
= 144

Answer(s): 144