Elijah, Ethan and Japheth have some beads. The ratios of their beads are as follows:

Elijah : (Elijah + Ethan + Japheth) = 2 : 5
Ethan : (Elijah + Japheth) = 1 : 5

Japheth has 64 beads more than Ethan. In the end, Japheth gives away all he has to Ethan and Elijah so that both Ethan and Elijah end up with the same number of beads, how many beads has Elijah received from Japheth?

Ethan	Japheth	Elijah	Total
3x6		2x6	5x6
1x5	5x5		6x5
5 u	13 u	12 u	30 u

The total number of beads is repeated.  Make the total number of beads the same.  LCM of 5 and 6 is 30.

Number of beads that Japheth has more than Ethan
= 13 u - 5 u
= 8 u

8 u = 64

1 u = 64 ÷ 8 = 8

	Ethan	Japheth	Elijah
Before	5 u	13 u	12 u
Change	+ 10 u	- 13 u	+ 3 u
After	15 u	0 u	15 u

Number of beads that Elijah has received from Japheth
= 15 u - 12 u 
= 3 u
= 3 x 8
= 24

Answer(s): 24