Nick, Gabriel and Charlie have some beads. The ratios of their beads are as follows:

Nick : (Nick + Gabriel + Charlie) = 1 : 4
Gabriel : (Nick + Charlie) = 1 : 4

Charlie has 42 beads more than Gabriel. In the end, Charlie gives away all he has to Gabriel and Nick so that both Gabriel and Nick end up with the same number of beads, how many beads has Nick received from Charlie?

Gabriel	Charlie	Nick	Total
3x5		1x5	4x5
1x4	4x4		5x4
4 u	11 u	5 u	20 u

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

Number of beads that Charlie has more than Gabriel
= 11 u - 4 u
= 7 u

7 u = 42

1 u = 42 ÷ 7 = 6

	Gabriel	Charlie	Nick
Before	4 u	11 u	5 u
Change	+ 6 u	- 11 u	+ 5 u
After	10 u	0 u	10 u

Number of beads that Nick has received from Charlie
= 10 u - 5 u 
= 5 u
= 5 x 6
= 30

Answer(s): 30