Hazel and Mary had a total of 90 pens. Mary gave ¹₃ of her pens to Hazel. In return, Hazel gave ¹₆ of the total number of pens that she had to Mary. In the end, each girl had the same number of pens. How many pens did Hazel have at first?

	Hazel	Mary	Total
Before 1	?	3 u	90
Change 1	+ 1 u	- 1 u
After 1	54	2 u	90
Before 2	6 p	2 u	90
Change 2	- 1 p	+ 1 p
After 2	5 p (45)	45	90

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

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

Number of pens that Hazel had in the end
= 90 ÷ 2
= 45

Number of pens that Hazel had in the end = 5 p

5 p = 45

1 p = 45 ÷ 5 = 9

Number of pens that Hazel had after receiving some pens from Mary
= 6 p
= 6 x 9
= 54

Number of pens that Mary had after giving to Hazel
= 90 - 54
= 36

2 u = 36

1 u = 36 ÷ 2 = 18

Number of pens that Mary had at first
= 3 u
= 3 x 18
= 54

Number of pens that Hazel had at first
= 90 - 54
= 36

Answer(s): 36