Dylan had ³₄ as many stickers as Peter. Peter had ⁴₇ as many stickers as Cathy. After Dylan and Cathy gave 8 stickers to Peter, Peter had thrice as many stickers as Dylan. Cathy then had the same number of stickers as Peter.

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

Dylan	Peter	Cathy
3	4
	4	7
3	4	7

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

Ratio of the number of stickers that Dylan had to the number of stickers that Cathy had in the beginning = 3 : 7

	Dylan	Peter	Cathy	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 Peter received from Dylan and Cathy
= 2 x 8
= 16

Number of stickers that Peter received from Dylan and Cathy
= 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