Xandra and Kimberly had a total of 80 coins. Kimberly gave ¹₃ of her coins to Xandra. In return, Xandra gave ¹₅ of the total number of coins that she had to Kimberly. In the end, each girl had the same number of coins. How many coins did Xandra have at first?

	Xandra	Kimberly	Total
Before 1	?	3 u	80
Change 1	+ 1 u	- 1 u
After 1	50	2 u	80
Before 2	5 p	2 u	80
Change 2	- 1 p	+ 1 p
After 2	4 p (40)	40	80

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

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

Number of coins that Xandra had in the end
= 80 ÷ 2
= 40

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

4 p = 40

1 p = 40 ÷ 4 = 10

Number of coins that Xandra had after receiving some coins from Kimberly
= 5 p
= 5 x 10
= 50

Number of coins that Kimberly had after giving to Xandra
= 80 - 50
= 30

2 u = 30

1 u = 30 ÷ 2 = 15

Number of coins that Kimberly had at first
= 3 u
= 3 x 15
= 45

Number of coins that Xandra had at first
= 80 - 45
= 35

Answer(s): 35