Liam had ¹₂ as many stickers as Neave. Neave had ²₃ as many stickers as Hilda. After Liam and Hilda gave 8 stickers to Neave, Neave had four times as many stickers as Liam. Hilda then had the same number of stickers as Neave.

1. What was the ratio of the number of stickers Hilda had to the number of stickers Liam had in the beginning? Answer in simplest form.
2. How many stickers did Neave have in the end?

Liam	Neave	Hilda
1	2
	2	3
1	2	3

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

Ratio of the number of stickers that Hilda had to the number of stickers that Liam had in the beginning = 3 : 1

	Liam	Neave	Hilda	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 Neave received from Liam and Hilda
= 2 x 8
= 16

Number of stickers that Neave received from Liam and Hilda
= 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