Carl had ¹₂ as many stamps as Pierre. Pierre had ²₃ as many stamps as Nicole. After Carl and Nicole gave 18 stamps to Pierre, Pierre had four times as many stamps as Carl. Nicole then had the same number of stamps as Pierre.

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

Carl	Pierre	Nicole
1	2
	2	3
1	2	3

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

Ratio of the number of stamps that Carl had to the number of stamps that Nicole had in the beginning = 1 : 3

	Carl	Pierre	Nicole	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 18	+ 36	- 18
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 Carl and Nicole
= 2 x 18
= 36

Number of stamps that Pierre received from Carl and Nicole
= 2 x 1 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

Number of stamps that Ashley had in the end
= 8 u
= 8 x 9
= 72