Riordan had ¹₂ as many pens as Julian. Julian had ²₃ as many pens as Pamela. After Riordan and Pamela gave 12 pens to Julian, Julian had four times as many pens as Riordan. Pamela then had the same number of pens as Julian.

1. What was the ratio of the number of pens Riordan had to the number of pens Pamela had in the beginning? Answer in simplest form.
2. How many pens did Julian have in the end?

Riordan	Julian	Pamela
1	2
	2	3
1	2	3

(a)
The number of pens that Julian is repeated.  

Ratio of the number of pens that Riordan had to the number of pens that Pamela had in the beginning = 1 : 3

	Riordan	Julian	Pamela	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 pens at first and in the end remains unchanged. Make the total number of pens the same. LCM of 6 and 9 is 18.

Number of pens that Julian received from Riordan and Pamela
= 2 x 12
= 24

Number of pens that Julian received from Riordan and Pamela
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

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