Zeph had ¹₂ as many beads as Carl. Carl had ²₃ as many beads as Yoko. After Zeph and Yoko gave 16 beads to Carl, Carl had four times as many beads as Zeph. Yoko then had the same number of beads as Carl.

1. What was the ratio of the number of beads Yoko had to the number of beads Zeph had in the beginning? Answer in simplest form.
2. How many beads did Carl have in the end?

Zeph	Carl	Yoko
1	2
	2	3
1	2	3

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

Ratio of the number of beads that Yoko had to the number of beads that Zeph had in the beginning = 3 : 1

	Zeph	Carl	Yoko	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 16	+ 32	- 16
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 Carl received from Zeph and Yoko
= 2 x 16
= 32

Number of beads that Carl received from Zeph and Yoko
= 2 x 1 u
= 2 u

2 u = 16

1 u = 16 ÷ 2 = 8

Number of beads that Ashley had in the end
= 8 u
= 8 x 8
= 64