Anna and Irene had a total of 60 cards. Irene gave ¹₅ of her cards to Anna. In return, Anna gave ¹₄ of the total number of cards that she had to Irene. In the end, each girl had the same number of cards. How many cards did Anna have at first?

	Anna	Irene	Total
Before 1	?	5 u	60
Change 1	+ 1 u	- 1 u
After 1	40	4 u	60
Before 2	4 p	4 u	60
Change 2	- 1 p	+ 1 p
After 2	3 p (30)	30	60

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

Number of cards that Irene and Anna each had in the end is the same.

Number of cards that Anna had in the end
= 60 ÷ 2
= 30

Number of cards that Anna had in the end = 3 p

3 p = 30

1 p = 30 ÷ 3 = 10

Number of cards that Anna had after receiving some cards from Irene
= 4 p
= 4 x 10
= 40

Number of cards that Irene had after giving to Anna
= 60 - 40
= 20

4 u = 20

1 u = 20 ÷ 4 = 5

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

Number of cards that Anna had at first
= 60 - 25
= 35

Answer(s): 35