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

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

Number of cards that Kylie and Sabrina each had in the end is the same.

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

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

7 p = 42

1 p = 42 ÷ 7 = 6

Number of cards that Sabrina had after receiving some cards from Kylie
= 8 p
= 8 x 6
= 48

Number of cards that Kylie had after giving to Sabrina
= 84 - 48
= 36

2 u = 36

1 u = 36 ÷ 2 = 18

Number of cards that Kylie had at first
= 3 u
= 3 x 18
= 54

Number of cards that Sabrina had at first
= 84 - 54
= 30

Answer(s): 30