Julian had ¹₂ as many beads as Caden. Caden had ²₃ as many beads as Opal. After Julian and Opal gave 16 beads to Caden, Caden had four times as many beads as Julian. Opal then had the same number of beads as Caden.

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

Julian	Caden	Opal
1	2
	2	3
1	2	3

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

Ratio of the number of beads that Julian had to the number of beads that Opal had in the beginning = 1 : 3

	Julian	Caden	Opal	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 Caden received from Julian and Opal
= 2 x 16
= 32

Number of beads that Caden received from Julian and Opal
= 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