Mark had ³₄ as many pens as Howard. Howard had ⁴₇ as many pens as Erika. After Mark and Erika gave 22 pens to Howard, Howard had thrice as many pens as Mark. Erika then had the same number of pens as Howard.

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

Mark	Howard	Erika
3	4
	4	7
3	4	7

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

Ratio of the number of pens that Erika had to the number of pens that Mark had in the beginning = 7 : 3

	Mark	Howard	Erika	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 22	+ 44	- 22
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of pens at first and in the end remains unchanged. Make the total number of pens the same. LCM of 14 and 7 is 14.

Number of pens that Howard received from Mark and Erika
= 2 x 22
= 44

Number of pens that Howard received from Mark and Erika
= 2 x 1 u
= 2 u

2 u = 22

1 u = 22 ÷ 2 = 11

Number of pens that Ashley had in the end
= 6 u
= 6 x 11
= 66