Andy had ¹₂ as many stamps as Pierre. Pierre had ²₃ as many stamps as Zoe. After Andy and Zoe gave 22 stamps to Pierre, Pierre had four times as many stamps as Andy. Zoe then had the same number of stamps as Pierre.

1. What was the ratio of the number of stamps Andy had to the number of stamps Zoe had in the beginning? Answer in simplest form.
2. How many stamps did Pierre have in the end?

Andy	Pierre	Zoe
1	2
	2	3
1	2	3

(a)
The number of stamps that Pierre is repeated.  

Ratio of the number of stamps that Andy had to the number of stamps that Zoe had in the beginning = 1 : 3

	Andy	Pierre	Zoe	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 22	+ 44	- 22
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of stamps at first and in the end remains unchanged. Make the total number of stamps the same. LCM of 6 and 9 is 18.

Number of stamps that Pierre received from Andy and Zoe
= 2 x 22
= 44

Number of stamps that Pierre received from Andy and Zoe
= 2 x 1 u
= 2 u

2 u = 22

1 u = 22 ÷ 2 = 11

Number of stamps that Ashley had in the end
= 8 u
= 8 x 11
= 88