Linda and Fiona had a total of 48 cards. Fiona gave ¹₅ of her cards to Linda. In return, Linda gave ¹₇ of the total number of cards that she had to Fiona. In the end, each girl had the same number of cards. How many cards did Linda have at first?

	Linda	Fiona	Total
Before 1	?	5 u	48
Change 1	+ 1 u	- 1 u
After 1	28	4 u	48
Before 2	7 p	4 u	48
Change 2	- 1 p	+ 1 p
After 2	6 p (24)	24	48

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

Number of cards that Fiona and Linda each had in the end is the same.

Number of cards that Linda had in the end
= 48 ÷ 2
= 24

Number of cards that Linda had in the end = 6 p

6 p = 24

1 p = 24 ÷ 6 = 4

Number of cards that Linda had after receiving some cards from Fiona
= 7 p
= 7 x 4
= 28

Number of cards that Fiona had after giving to Linda
= 48 - 28
= 20

4 u = 20

1 u = 20 ÷ 4 = 5

Number of cards that Fiona had at first
= 5 u
= 5 x 5
= 25

Number of cards that Linda had at first
= 48 - 25
= 23

Answer(s): 23