Lynn and Anna had a total of 36 pens. Anna gave ¹₄ of her pens to Lynn. In return, Lynn gave ¹₃ of the total number of pens that she had to Anna. In the end, each girl had the same number of pens. How many pens did Lynn have at first?

	Lynn	Anna	Total
Before 1	?	4 u	36
Change 1	+ 1 u	- 1 u
After 1	27	3 u	36
Before 2	3 p	3 u	36
Change 2	- 1 p	+ 1 p
After 2	2 p (18)	18	36

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

Number of pens that Anna and Lynn each had in the end is the same.

Number of pens that Lynn had in the end
= 36 ÷ 2
= 18

Number of pens that Lynn had in the end = 2 p

2 p = 18

1 p = 18 ÷ 2 = 9

Number of pens that Lynn had after receiving some pens from Anna
= 3 p
= 3 x 9
= 27

Number of pens that Anna had after giving to Lynn
= 36 - 27
= 9

3 u = 9

1 u = 9 ÷ 3 = 3

Number of pens that Anna had at first
= 4 u
= 4 x 3
= 12

Number of pens that Lynn had at first
= 36 - 12
= 24

Answer(s): 24