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

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

Number of cards that Barbara and Lynn each had in the end is the same.

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

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

2 p = 18

1 p = 18 ÷ 2 = 9

Number of cards that Lynn had after receiving some cards from Barbara
= 3 p
= 3 x 9
= 27

Number of cards that Barbara had after giving to Lynn
= 36 - 27
= 9

3 u = 9

1 u = 9 ÷ 3 = 3

Number of cards that Barbara had at first
= 4 u
= 4 x 3
= 12

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

Answer(s): 24