Riordan and Charlie shared some beads in the ratio of 3 : 7. After both each gave away 45 beads to their cousin, the ratio of the number of beads Riordan had to the total number of beads left was 1 : 5. How many beads did the two boys have in the end?

	Riordan	Charlie	Difference
Before	3x3 = 9 u	7x3 = 21 u	4x3 = 12 u
Change	- 45	- 45
After	1x4 = 4 u	4x4 = 16 u	3x4 = 12 u

Number of beads that Riordan and Charlie each gave to their cousin is the same.

The difference in the number of beads at first and in the end between Riordan and Charlie remains unchanged.  Make the difference in the number of beads the same.  LCM of 4 and 3 is 12.

Number of beads that Riordan gave to their cousin
= 9 u - 4 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

Number of beads that the two boys had in the end
= 4 u + 16 u
= 20 u
= 20 x 9
= 180

Answer(s): 180