Howard, Caden and Justin have some beads. The ratios of their beads are as follows:

Howard : (Howard + Caden + Justin) = 3 : 7
Caden : (Howard + Justin) = 1 : 5

Justin has 100 beads more than Caden. In the end, Justin gives away all he has to Caden and Howard so that both Caden and Howard end up with the same number of beads, how many beads has Caden received from Justin?

Caden	Justin	Howard	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 Justin has more than Caden
= 17 u - 7 u
= 10 u

10 u = 100

1 u = 100 ÷ 10 = 10

	Caden	Justin	Howard
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 Caden has received from Justin
= 21 u - 7 u 
= 14 u
= 14 x 10
= 140

Answer(s): 140