Liam and Jenson shared some marbles in the ratio of 5 : 7. After both each gave away 156 marbles to their cousin, the ratio of the number of marbles Liam had to the total number of marbles left was 1 : 5. How many marbles did the two boys have at first?

	Liam	Jenson	Difference
Before	5x3 = 15 u	7x3 = 21 u	2x3 = 6 u
Change	- 156	- 156
After	1x2 = 2 u	4x2 = 8 u	3x2 = 6 u

Number of marbles that Liam and Jenson each gave to their cousin is the same.

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

Number of marbles that Liam gave to their cousin
= 15 u - 2 u
= 13 u

13 u = 156

1 u = 156 ÷ 13 = 12

Number of marbles that the two boys had at first
= 15 u + 21 u
= 36 u
= 36 x 12
= 432

Answer(s): 432