David had ³₄ as many stickers as Gabriel. Gabriel had ⁴₇ as many stickers as Cathy. After David and Cathy gave 28 stickers to Gabriel, Gabriel had thrice as many stickers as David. Cathy then had the same number of stickers as Gabriel.

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

David	Gabriel	Cathy
3	4
	4	7
3	4	7

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

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

	David	Gabriel	Cathy	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 28	+ 56	- 28
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 Gabriel received from David and Cathy
= 2 x 28
= 56

Number of stickers that Gabriel received from David and Cathy
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of stickers that Ashley had in the end
= 6 u
= 6 x 14
= 84