Joelle and Olivia had a total of 144 cards. Olivia gave ¹₅ of her cards to Joelle. In return, Joelle gave ¹₇ of the total number of cards that she had to Olivia. In the end, each girl had the same number of cards. How many cards did Joelle have at first?

	Joelle	Olivia	Total
Before 1	?	5 u	144
Change 1	+ 1 u	- 1 u
After 1	84	4 u	144
Before 2	7 p	4 u	144
Change 2	- 1 p	+ 1 p
After 2	6 p (72)	72	144

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

Number of cards that Olivia and Joelle each had in the end is the same.

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

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

6 p = 72

1 p = 72 ÷ 6 = 12

Number of cards that Joelle had after receiving some cards from Olivia
= 7 p
= 7 x 12
= 84

Number of cards that Olivia had after giving to Joelle
= 144 - 84
= 60

4 u = 60

1 u = 60 ÷ 4 = 15

Number of cards that Olivia had at first
= 5 u
= 5 x 15
= 75

Number of cards that Joelle had at first
= 144 - 75
= 69

Answer(s): 69