Japheth had ¹₂ as many beads as Simon. Simon had ²₃ as many beads as Kylie. After Japheth and Kylie gave 4 beads to Simon, Simon had four times as many beads as Japheth. Kylie then had the same number of beads as Simon.

1. What was the ratio of the number of beads Japheth had to the number of beads Kylie had in the beginning? Answer in simplest form.
2. How many beads did Simon have in the end?

Japheth	Simon	Kylie
1	2
	2	3
1	2	3

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

Ratio of the number of beads that Japheth had to the number of beads that Kylie had in the beginning = 1 : 3

	Japheth	Simon	Kylie	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 4	+ 8	- 4
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 Simon received from Japheth and Kylie
= 2 x 4
= 8

Number of beads that Simon received from Japheth and Kylie
= 2 x 1 u
= 2 u

2 u = 4

1 u = 4 ÷ 2 = 2

Number of beads that Ashley had in the end
= 8 u
= 8 x 2
= 16