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

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

Jeremy	Riordan	Barbara
1	2
	2	3
1	2	3

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

Ratio of the number of stamps that Barbara had to the number of stamps that Jeremy had in the beginning = 3 : 1

	Jeremy	Riordan	Barbara	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 12	+ 24	- 12
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 Riordan received from Jeremy and Barbara
= 2 x 12
= 24

Number of stamps that Riordan received from Jeremy and Barbara
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

Number of stamps that Ashley had in the end
= 8 u
= 8 x 6
= 48