Pierre, Japheth and Michael have some beads. The ratios of their beads are as follows:

Pierre : (Pierre + Japheth + Michael) = 2 : 5
Japheth : (Pierre + Michael) = 1 : 3

Michael has 8 beads more than Japheth. In the end, Michael gives away all he has to Japheth and Pierre so that both Japheth and Pierre end up with the same number of beads, how many beads has Pierre received from Michael?

Japheth	Michael	Pierre	Total
3x4		2x4	5x4
1x5	3x5		4x5
5 u	7 u	8 u	20 u

The total number of beads is repeated.  Make the total number of beads the same.  LCM of 5 and 4 is 20.

Number of beads that Michael has more than Japheth
= 7 u - 5 u
= 2 u

2 u = 8

1 u = 8 ÷ 2 = 4

	Japheth	Michael	Pierre
Before	5 u	7 u	8 u
Change	+ 5 u	- 7 u	+ 2 u
After	10 u	0 u	10 u

Number of beads that Pierre has received from Michael
= 10 u - 8 u 
= 2 u
= 2 x 4
= 8

Answer(s): 8