John, Michael and Riordan have some beads. The ratios of their beads are as follows:

John : (John + Michael + Riordan) = 3 : 7
Michael : (John + Riordan) = 1 : 5

Riordan has 80 beads more than Michael. In the end, Riordan gives away all he has to Michael and John so that both Michael and John end up with the same number of beads, how many beads has John received from Riordan?

Michael	Riordan	John	Total
4x6		3x6	7x6
1x7	5x7		6x7
7 u	17 u	18 u	42 u

The total number of beads is repeated.  Make the total number of beads the same.  LCM of 7 and 6 is 42.

Number of beads that Riordan has more than Michael
= 17 u - 7 u
= 10 u

10 u = 80

1 u = 80 ÷ 10 = 8

	Michael	Riordan	John
Before	7 u	17 u	18 u
Change	+ 14 u	- 17 u	+ 3 u
After	21 u	0 u	21 u

Number of beads that John has received from Riordan
= 21 u - 18 u 
= 3 u
= 3 x 8
= 24

Answer(s): 24