Riordan had ¹₂ as many stamps as Seth. Seth had ²₃ as many stamps as Jen. After Riordan and Jen gave 18 stamps to Seth, Seth had four times as many stamps as Riordan. Jen then had the same number of stamps as Seth.

1. What was the ratio of the number of stamps Riordan had to the number of stamps Jen had in the beginning? Answer in simplest form.
2. How many stamps did Seth have in the end?

Riordan	Seth	Jen
1	2
	2	3
1	2	3

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

Ratio of the number of stamps that Riordan had to the number of stamps that Jen had in the beginning = 1 : 3

	Riordan	Seth	Jen	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 Seth received from Riordan and Jen
= 2 x 18
= 36

Number of stamps that Seth received from Riordan and Jen
= 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