Luke and Pierre shared some marbles in the ratio of 5 : 8. After both each gave away 85 marbles to their sister, the ratio of the number of marbles Luke had to the total number of marbles left was 1 : 6. How many marbles did the two boys have at first?

	Luke	Pierre	Difference
Before	5x4 = 20 u	8x4 = 32 u	3x4 = 12 u
Change	- 85	- 85
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of marbles that Luke and Pierre each gave to their sister is the same.

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

Number of marbles that Luke gave to their sister
= 20 u - 3 u
= 17 u

17 u = 85

1 u = 85 ÷ 17 = 5

Number of marbles that the two boys had at first
= 20 u + 32 u
= 52 u
= 52 x 5
= 260

Answer(s): 260