Raeann and Xylia had a total of 56 cards. Xylia gave ¹₄ of her cards to Raeann. In return, Raeann gave ¹₈ of the total number of cards that she had to Xylia. In the end, each girl had the same number of cards. How many cards did Raeann have at first?

	Raeann	Xylia	Total
Before 1	?	4 u	56
Change 1	+ 1 u	- 1 u
After 1	32	3 u	56
Before 2	8 p	3 u	56
Change 2	- 1 p	+ 1 p
After 2	7 p (28)	28	56

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

Number of cards that Xylia and Raeann each had in the end is the same.

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

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

7 p = 28

1 p = 28 ÷ 7 = 4

Number of cards that Raeann had after receiving some cards from Xylia
= 8 p
= 8 x 4
= 32

Number of cards that Xylia had after giving to Raeann
= 56 - 32
= 24

3 u = 24

1 u = 24 ÷ 3 = 8

Number of cards that Xylia had at first
= 4 u
= 4 x 8
= 32

Number of cards that Raeann had at first
= 56 - 32
= 24

Answer(s): 24