Julian and Michael shared some marbles in the ratio of 3 : 8. After both each gave away 42 marbles to their brother, the ratio of the number of marbles Julian had to the total number of marbles left was 1 : 6. How many marbles did the two boys have at first?

	Julian	Michael	Difference
Before	3x4 = 12 u	8x4 = 32 u	5x4 = 20 u
Change	- 42	- 42
After	1x5 = 5 u	5x5 = 25 u	4x5 = 20 u

Number of marbles that Julian and Michael each gave to their brother is the same.

The difference in the number of marbles at first and in the end between Julian and Michael remains unchanged.  Make the difference in the number of marbles the same.  LCM of 5 and 4 is 20.

Number of marbles that Julian gave to their brother
= 12 u - 5 u
= 7 u

7 u = 42

1 u = 42 ÷ 7 = 6

Number of marbles that the two boys had at first
= 12 u + 32 u
= 44 u
= 44 x 6
= 264

Answer(s): 264