Howard and Reggie shared some marbles in the ratio of 5 : 7. After both each gave away 104 marbles to their sister, the ratio of the number of marbles Howard had to the total number of marbles left was 1 : 5. How many marbles did the two boys have at first?

	Howard	Reggie	Difference
Before	5x3 = 15 u	7x3 = 21 u	2x3 = 6 u
Change	- 104	- 104
After	1x2 = 2 u	4x2 = 8 u	3x2 = 6 u

Number of marbles that Howard and Reggie each gave to their sister is the same.

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

Number of marbles that Howard gave to their sister
= 15 u - 2 u
= 13 u

13 u = 104

1 u = 104 ÷ 13 = 8

Number of marbles that the two boys had at first
= 15 u + 21 u
= 36 u
= 36 x 8
= 288

Answer(s): 288