Caden had ¹₂ as many beads as Will. Will had ²₃ as many beads as Marion. After Caden and Marion gave 14 beads to Will, Will had four times as many beads as Caden. Marion then had the same number of beads as Will.

1. What was the ratio of the number of beads Marion had to the number of beads Caden had in the beginning? Answer in simplest form.
2. How many beads did Will have in the end?

Caden	Will	Marion
1	2
	2	3
1	2	3

(a)
The number of beads that Will is repeated.  

Ratio of the number of beads that Marion had to the number of beads that Caden had in the beginning = 3 : 1

	Caden	Will	Marion	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 14	+ 28	- 14
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of beads at first and in the end remains unchanged. Make the total number of beads the same. LCM of 6 and 9 is 18.

Number of beads that Will received from Caden and Marion
= 2 x 14
= 28

Number of beads that Will received from Caden and Marion
= 2 x 1 u
= 2 u

2 u = 14

1 u = 14 ÷ 2 = 7

Number of beads that Ashley had in the end
= 8 u
= 8 x 7
= 56