Ryan and Japheth shared some marbles in the ratio of 4 : 7. After both each gave away 45 marbles to their brother, the ratio of the number of marbles Ryan had to the total number of marbles left was 1 : 4. How many marbles did the two boys have in the end?

	Ryan	Japheth	Difference
Before	4x2 = 8 u	7x2 = 14 u	3x2 = 6 u
Change	- 45	- 45
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of marbles that Ryan and Japheth each gave to their brother is the same.

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

Number of marbles that Ryan gave to their brother
= 8 u - 3 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

Number of marbles that the two boys had in the end
= 3 u + 9 u
= 12 u
= 12 x 9
= 108

Answer(s): 108