Sean had ¹₂ as many pens as Howard. Howard had ²₃ as many pens as Xandra. After Sean and Xandra gave 16 pens to Howard, Howard had four times as many pens as Sean. Xandra then had the same number of pens as Howard.

1. What was the ratio of the number of pens Xandra had to the number of pens Sean had in the beginning? Answer in simplest form.
2. How many pens did Howard have in the end?

Sean	Howard	Xandra
1	2
	2	3
1	2	3

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

Ratio of the number of pens that Xandra had to the number of pens that Sean had in the beginning = 3 : 1

	Sean	Howard	Xandra	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 16	+ 32	- 16
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 Howard received from Sean and Xandra
= 2 x 16
= 32

Number of pens that Howard received from Sean and Xandra
= 2 x 1 u
= 2 u

2 u = 16

1 u = 16 ÷ 2 = 8

Number of pens that Ashley had in the end
= 8 u
= 8 x 8
= 64