Kimberly and Fanny had a total of 60 coins. Fanny gave ¹₅ of her coins to Kimberly. In return, Kimberly gave ¹₄ of the total number of coins that she had to Fanny. In the end, each girl had the same number of coins. How many coins did Kimberly have at first?

	Kimberly	Fanny	Total
Before 1	?	5 u	60
Change 1	+ 1 u	- 1 u
After 1	40	4 u	60
Before 2	4 p	4 u	60
Change 2	- 1 p	+ 1 p
After 2	3 p (30)	30	60

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

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

Number of coins that Kimberly had in the end
= 60 ÷ 2
= 30

Number of coins that Kimberly had in the end = 3 p

3 p = 30

1 p = 30 ÷ 3 = 10

Number of coins that Kimberly had after receiving some coins from Fanny
= 4 p
= 4 x 10
= 40

Number of coins that Fanny had after giving to Kimberly
= 60 - 40
= 20

4 u = 20

1 u = 20 ÷ 4 = 5

Number of coins that Fanny had at first
= 5 u
= 5 x 5
= 25

Number of coins that Kimberly had at first
= 60 - 25
= 35

Answer(s): 35