Rachel and Winnie had a total of 36 cards. Winnie gave ¹₄ of her cards to Rachel. In return, Rachel gave ¹₇ of the total number of cards that she had to Winnie. In the end, each girl had the same number of cards. How many cards did Rachel have at first?

	Rachel	Winnie	Total
Before 1	?	4 u	36
Change 1	+ 1 u	- 1 u
After 1	21	3 u	36
Before 2	7 p	3 u	36
Change 2	- 1 p	+ 1 p
After 2	6 p (18)	18	36

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

Number of cards that Winnie and Rachel each had in the end is the same.

Number of cards that Rachel had in the end
= 36 ÷ 2
= 18

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

6 p = 18

1 p = 18 ÷ 6 = 3

Number of cards that Rachel had after receiving some cards from Winnie
= 7 p
= 7 x 3
= 21

Number of cards that Winnie had after giving to Rachel
= 36 - 21
= 15

3 u = 15

1 u = 15 ÷ 3 = 5

Number of cards that Winnie had at first
= 4 u
= 4 x 5
= 20

Number of cards that Rachel had at first
= 36 - 20
= 16

Answer(s): 16