Gabby and Erika had a total of 98 cards. Erika gave ¹₃ of her cards to Gabby. In return, Gabby gave ¹₈ of the total number of cards that she had to Erika. In the end, each girl had the same number of cards. How many cards did Gabby have at first?

	Gabby	Erika	Total
Before 1	?	3 u	98
Change 1	+ 1 u	- 1 u
After 1	56	2 u	98
Before 2	8 p	2 u	98
Change 2	- 1 p	+ 1 p
After 2	7 p (49)	49	98

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

Number of cards that Erika and Gabby each had in the end is the same.

Number of cards that Gabby had in the end
= 98 ÷ 2
= 49

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

7 p = 49

1 p = 49 ÷ 7 = 7

Number of cards that Gabby had after receiving some cards from Erika
= 8 p
= 8 x 7
= 56

Number of cards that Erika had after giving to Gabby
= 98 - 56
= 42

2 u = 42

1 u = 42 ÷ 2 = 21

Number of cards that Erika had at first
= 3 u
= 3 x 21
= 63

Number of cards that Gabby had at first
= 98 - 63
= 35

Answer(s): 35