Xavier and Rael shared some marbles in the ratio of 5 : 7. After both each gave away 24 marbles to their cousin, the ratio of the number of marbles Xavier had to the total number of marbles left was 1 : 3. How many marbles did the two boys have in the end?

	Xavier	Rael	Difference
Before	5x1 = 5 u	7x1 = 7 u	2x1 = 2 u
Change	- 24	- 24
After	1x2 = 2 u	2x2 = 4 u	1x2 = 2 u

Number of marbles that Xavier and Rael each gave to their cousin is the same.

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

Number of marbles that Xavier gave to their cousin
= 5 u - 2 u
= 3 u

3 u = 24

1 u = 24 ÷ 3 = 8

Number of marbles that the two boys had in the end
= 2 u + 4 u
= 6 u
= 6 x 8
= 48

Answer(s): 48