Glen had ¹₂ as many pens as Julian. Julian had ²₃ as many pens as Elyse. After Glen and Elyse gave 8 pens to Julian, Julian had four times as many pens as Glen. Elyse then had the same number of pens as Julian.

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

Glen	Julian	Elyse
1	2
	2	3
1	2	3

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

Ratio of the number of pens that Glen had to the number of pens that Elyse had in the beginning = 1 : 3

	Glen	Julian	Elyse	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 8	+ 16	- 8
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 Glen and Elyse
= 2 x 8
= 16

Number of pens that Julian received from Glen and Elyse
= 2 x 1 u
= 2 u

2 u = 8

1 u = 8 ÷ 2 = 4

Number of pens that Ashley had in the end
= 8 u
= 8 x 4
= 32