Hazel and Roshel had a total of 80 pens. Roshel gave ¹₆ of her pens to Hazel. In return, Hazel gave ¹₅ of the total number of pens that she had to Roshel. In the end, each girl had the same number of pens. How many pens did Hazel have at first?

	Hazel	Roshel	Total
Before 1	?	6 u	80
Change 1	+ 1 u	- 1 u
After 1	50	5 u	80
Before 2	5 p	5 u	80
Change 2	- 1 p	+ 1 p
After 2	4 p (40)	40	80

Since Roshel gave some pens to Hazel and Hazel then gave some pens to Roshel, it is an internal transfer of pens between the two girls. So, the total number of pens remains unchanged.

Number of pens that Roshel and Hazel each had in the end is the same.

Number of pens that Hazel had in the end
= 80 ÷ 2
= 40

Number of pens that Hazel had in the end = 4 p

4 p = 40

1 p = 40 ÷ 4 = 10

Number of pens that Hazel had after receiving some pens from Roshel
= 5 p
= 5 x 10
= 50

Number of pens that Roshel had after giving to Hazel
= 80 - 50
= 30

5 u = 30

1 u = 30 ÷ 5 = 6

Number of pens that Roshel had at first
= 6 u
= 6 x 6
= 36

Number of pens that Hazel had at first
= 80 - 36
= 44

Answer(s): 44