Tina and Xandra had a total of 96 coins. Xandra gave ¹₃ of her coins to Tina. In return, Tina gave ¹₅ of the total number of coins that she had to Xandra. In the end, each girl had the same number of coins. How many coins did Tina have at first?

	Tina	Xandra	Total
Before 1	?	3 u	96
Change 1	+ 1 u	- 1 u
After 1	60	2 u	96
Before 2	5 p	2 u	96
Change 2	- 1 p	+ 1 p
After 2	4 p (48)	48	96

Since Xandra gave some coins to Tina and Tina then gave some coins to Xandra, it is an internal transfer of coins between the two girls. So, the total number of coins remains unchanged.

Number of coins that Xandra and Tina each had in the end is the same.

Number of coins that Tina had in the end
= 96 ÷ 2
= 48

Number of coins that Tina had in the end = 4 p

4 p = 48

1 p = 48 ÷ 4 = 12

Number of coins that Tina had after receiving some coins from Xandra
= 5 p
= 5 x 12
= 60

Number of coins that Xandra had after giving to Tina
= 96 - 60
= 36

2 u = 36

1 u = 36 ÷ 2 = 18

Number of coins that Xandra had at first
= 3 u
= 3 x 18
= 54

Number of coins that Tina had at first
= 96 - 54
= 42

Answer(s): 42