Xavier and Valen shared some marbles in the ratio of 3 : 7. After both each gave away 55 marbles to their sister, the ratio of the number of marbles Xavier had to the total number of marbles left was 1 : 5. How many marbles did the two boys have in the end?

	Xavier	Valen	Difference
Before	3x3 = 9 u	7x3 = 21 u	4x3 = 12 u
Change	- 55	- 55
After	1x4 = 4 u	4x4 = 16 u	3x4 = 12 u

Number of marbles that Xavier and Valen each gave to their sister is the same.

The difference in the number of marbles at first and in the end between Xavier and Valen remains unchanged.  Make the difference in the number of marbles the same.  LCM of 4 and 3 is 12.

Number of marbles that Xavier gave to their sister
= 9 u - 4 u
= 5 u

5 u = 55

1 u = 55 ÷ 5 = 11

Number of marbles that the two boys had in the end
= 4 u + 16 u
= 20 u
= 20 x 11
= 220

Answer(s): 220