Valen and Elijah shared some marbles in the ratio of 5 : 7. After both each gave away 27 marbles to their sister, the ratio of the number of marbles Valen had to the total number of marbles left was 1 : 3. How many marbles did the two boys have at first?

	Valen	Elijah	Difference
Before	5x1 = 5 u	7x1 = 7 u	2x1 = 2 u
Change	- 27	- 27
After	1x2 = 2 u	2x2 = 4 u	1x2 = 2 u

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

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

Number of marbles that Valen gave to their sister
= 5 u - 2 u
= 3 u

3 u = 27

1 u = 27 ÷ 3 = 9

Number of marbles that the two boys had at first
= 5 u + 7 u
= 12 u
= 12 x 9
= 108

Answer(s): 108