Cody had ¹₂ as many beads as Ian. Ian had ²₃ as many beads as Zoe. After Cody and Zoe gave 26 beads to Ian, Ian had four times as many beads as Cody. Zoe then had the same number of beads as Ian.

1. What was the ratio of the number of beads Zoe had to the number of beads Cody had in the beginning? Answer in simplest form.
2. How many beads did Ian have in the end?

Cody	Ian	Zoe
1	2
	2	3
1	2	3

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

Ratio of the number of beads that Zoe had to the number of beads that Cody had in the beginning = 3 : 1

	Cody	Ian	Zoe	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 26	+ 52	- 26
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 Ian received from Cody and Zoe
= 2 x 26
= 52

Number of beads that Ian received from Cody and Zoe
= 2 x 1 u
= 2 u

2 u = 26

1 u = 26 ÷ 2 = 13

Number of beads that Ashley had in the end
= 8 u
= 8 x 13
= 104