Erika and Diana had a total of 84 pens. Diana gave ¹₃ of her pens to Erika. In return, Erika gave ¹₈ of the total number of pens that she had to Diana. In the end, each girl had the same number of pens. How many pens did Erika have at first?

	Erika	Diana	Total
Before 1	?	3 u	84
Change 1	+ 1 u	- 1 u
After 1	48	2 u	84
Before 2	8 p	2 u	84
Change 2	- 1 p	+ 1 p
After 2	7 p (42)	42	84

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

Number of pens that Diana and Erika each had in the end is the same.

Number of pens that Erika had in the end
= 84 ÷ 2
= 42

Number of pens that Erika had in the end = 7 p

7 p = 42

1 p = 42 ÷ 7 = 6

Number of pens that Erika had after receiving some pens from Diana
= 8 p
= 8 x 6
= 48

Number of pens that Diana had after giving to Erika
= 84 - 48
= 36

2 u = 36

1 u = 36 ÷ 2 = 18

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

Number of pens that Erika had at first
= 84 - 54
= 30

Answer(s): 30