Sam and Billy shared some marbles in the ratio of 5 : 7. After both each gave away 6 marbles to their brother, the ratio of the number of marbles Sam had to the total number of marbles left was 1 : 3. How many marbles did the two boys have at first?

	Sam	Billy	Difference
Before	5x1 = 5 u	7x1 = 7 u	2x1 = 2 u
Change	- 6	- 6
After	1x2 = 2 u	2x2 = 4 u	1x2 = 2 u

Number of marbles that Sam and Billy each gave to their brother is the same.

The difference in the number of marbles at first and in the end between Sam and Billy remains unchanged.  Make the difference in the number of marbles the same.  LCM of 2 and 1 is 2.

Number of marbles that Sam gave to their brother
= 5 u - 2 u
= 3 u

3 u = 6

1 u = 6 ÷ 3 = 2

Number of marbles that the two boys had at first
= 5 u + 7 u
= 12 u
= 12 x 2
= 24

Answer(s): 24