Sabrina and Kathy had a total of 56 cards. Kathy gave ¹₅ of her cards to Sabrina. In return, Sabrina gave ¹₈ of the total number of cards that she had to Kathy. In the end, each girl had the same number of cards. How many cards did Sabrina have at first?

	Sabrina	Kathy	Total
Before 1	?	5 u	56
Change 1	+ 1 u	- 1 u
After 1	32	4 u	56
Before 2	8 p	4 u	56
Change 2	- 1 p	+ 1 p
After 2	7 p (28)	28	56

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

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

Number of cards that Sabrina had in the end
= 56 ÷ 2
= 28

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

7 p = 28

1 p = 28 ÷ 7 = 4

Number of cards that Sabrina had after receiving some cards from Kathy
= 8 p
= 8 x 4
= 32

Number of cards that Kathy had after giving to Sabrina
= 56 - 32
= 24

4 u = 24

1 u = 24 ÷ 4 = 6

Number of cards that Kathy had at first
= 5 u
= 5 x 6
= 30

Number of cards that Sabrina had at first
= 56 - 30
= 26

Answer(s): 26