Jaslyn and Vanessa had a total of 84 cards. Vanessa gave ¹₄ of her cards to Jaslyn. In return, Jaslyn gave ¹₈ of the total number of cards that she had to Vanessa. In the end, each girl had the same number of cards. How many cards did Jaslyn have at first?

	Jaslyn	Vanessa	Total
Before 1	?	4 u	84
Change 1	+ 1 u	- 1 u
After 1	48	3 u	84
Before 2	8 p	3 u	84
Change 2	- 1 p	+ 1 p
After 2	7 p (42)	42	84

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

Number of cards that Vanessa and Jaslyn each had in the end is the same.

Number of cards that Jaslyn had in the end
= 84 ÷ 2
= 42

Number of cards that Jaslyn had in the end = 7 p

7 p = 42

1 p = 42 ÷ 7 = 6

Number of cards that Jaslyn had after receiving some cards from Vanessa
= 8 p
= 8 x 6
= 48

Number of cards that Vanessa had after giving to Jaslyn
= 84 - 48
= 36

3 u = 36

1 u = 36 ÷ 3 = 12

Number of cards that Vanessa had at first
= 4 u
= 4 x 12
= 48

Number of cards that Jaslyn had at first
= 84 - 48
= 36

Answer(s): 36