Sarah and Lynn had a total of 144 cards. Lynn gave ¹₃ of her cards to Sarah. In return, Sarah gave ¹₇ of the total number of cards that she had to Lynn. In the end, each girl had the same number of cards. How many cards did Sarah have at first?

	Sarah	Lynn	Total
Before 1	?	3 u	144
Change 1	+ 1 u	- 1 u
After 1	84	2 u	144
Before 2	7 p	2 u	144
Change 2	- 1 p	+ 1 p
After 2	6 p (72)	72	144

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

Number of cards that Lynn and Sarah each had in the end is the same.

Number of cards that Sarah had in the end
= 144 ÷ 2
= 72

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

6 p = 72

1 p = 72 ÷ 6 = 12

Number of cards that Sarah had after receiving some cards from Lynn
= 7 p
= 7 x 12
= 84

Number of cards that Lynn had after giving to Sarah
= 144 - 84
= 60

2 u = 60

1 u = 60 ÷ 2 = 30

Number of cards that Lynn had at first
= 3 u
= 3 x 30
= 90

Number of cards that Sarah had at first
= 144 - 90
= 54

Answer(s): 54