Paul had ³₄ as many stickers as Harry. Harry had ⁴₇ as many stickers as Natalie. After Paul and Natalie gave 12 stickers to Harry, Harry had thrice as many stickers as Paul. Natalie then had the same number of stickers as Harry.

1. What was the ratio of the number of stickers Paul had to the number of stickers Natalie had in the beginning? Answer in simplest form.
2. How many stickers did Harry have in the end?

Paul	Harry	Natalie
3	4
	4	7
3	4	7

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

Ratio of the number of stickers that Paul had to the number of stickers that Natalie had in the beginning = 3 : 7

	Paul	Harry	Natalie	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 12	+ 24	- 12
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 Harry received from Paul and Natalie
= 2 x 12
= 24

Number of stickers that Harry received from Paul and Natalie
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

Number of stickers that Ashley had in the end
= 6 u
= 6 x 6
= 36