Cathy and Risa had a total of 60 pens. Risa gave ¹₃ of her pens to Cathy. In return, Cathy gave ¹₆ of the total number of pens that she had to Risa. In the end, each girl had the same number of pens. How many pens did Cathy have at first?

	Cathy	Risa	Total
Before 1	?	3 u	60
Change 1	+ 1 u	- 1 u
After 1	36	2 u	60
Before 2	6 p	2 u	60
Change 2	- 1 p	+ 1 p
After 2	5 p (30)	30	60

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

Number of pens that Risa and Cathy each had in the end is the same.

Number of pens that Cathy had in the end
= 60 ÷ 2
= 30

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

5 p = 30

1 p = 30 ÷ 5 = 6

Number of pens that Cathy had after receiving some pens from Risa
= 6 p
= 6 x 6
= 36

Number of pens that Risa had after giving to Cathy
= 60 - 36
= 24

2 u = 24

1 u = 24 ÷ 2 = 12

Number of pens that Risa had at first
= 3 u
= 3 x 12
= 36

Number of pens that Cathy had at first
= 60 - 36
= 24

Answer(s): 24