Jack had ¹₂ as many stickers as Dylan. Dylan had ²₃ as many stickers as Vanessa. After Jack and Vanessa gave 8 stickers to Dylan, Dylan had four times as many stickers as Jack. Vanessa then had the same number of stickers as Dylan.

1. What was the ratio of the number of stickers Jack had to the number of stickers Vanessa had in the beginning? Answer in simplest form.
2. How many stickers did Dylan have in the end?

Jack	Dylan	Vanessa
1	2
	2	3
1	2	3

(a)
The number of stickers that Dylan is repeated.  

Ratio of the number of stickers that Jack had to the number of stickers that Vanessa had in the beginning = 1 : 3

	Jack	Dylan	Vanessa	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 8	+ 16	- 8
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

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

Number of stickers that Dylan received from Jack and Vanessa
= 2 x 8
= 16

Number of stickers that Dylan received from Jack and Vanessa
= 2 x 1 u
= 2 u

2 u = 8

1 u = 8 ÷ 2 = 4

Number of stickers that Ashley had in the end
= 8 u
= 8 x 4
= 32