Valen had ³₄ as many stickers as Jenson. Jenson had ⁴₇ as many stickers as Penelope. After Valen and Penelope gave 8 stickers to Jenson, Jenson had thrice as many stickers as Valen. Penelope then had the same number of stickers as Jenson.

1. What was the ratio of the number of stickers Penelope had to the number of stickers Valen had in the beginning? Answer in simplest form.
2. How many stickers did Jenson have in the end?

Valen	Jenson	Penelope
3	4
	4	7
3	4	7

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

Ratio of the number of stickers that Penelope had to the number of stickers that Valen had in the beginning = 7 : 3

	Valen	Jenson	Penelope	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 8	+ 16	- 8
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of stickers at first and in the end remains unchanged. Make the total number of stickers the same. LCM of 14 and 7 is 14.

Number of stickers that Jenson received from Valen and Penelope
= 2 x 8
= 16

Number of stickers that Jenson received from Valen and Penelope
= 2 x 1 u
= 2 u

2 u = 8

1 u = 8 ÷ 2 = 4

Number of stickers that Ashley had in the end
= 6 u
= 6 x 4
= 24