Kimberly and Jane had a total of 112 coins. Jane gave ¹₅ of her coins to Kimberly. In return, Kimberly gave ¹₈ of the total number of coins that she had to Jane. In the end, each girl had the same number of coins. How many coins did Kimberly have at first?

	Kimberly	Jane	Total
Before 1	?	5 u	112
Change 1	+ 1 u	- 1 u
After 1	64	4 u	112
Before 2	8 p	4 u	112
Change 2	- 1 p	+ 1 p
After 2	7 p (56)	56	112

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

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

Number of coins that Kimberly had in the end
= 112 ÷ 2
= 56

Number of coins that Kimberly had in the end = 7 p

7 p = 56

1 p = 56 ÷ 7 = 8

Number of coins that Kimberly had after receiving some coins from Jane
= 8 p
= 8 x 8
= 64

Number of coins that Jane had after giving to Kimberly
= 112 - 64
= 48

4 u = 48

1 u = 48 ÷ 4 = 12

Number of coins that Jane had at first
= 5 u
= 5 x 12
= 60

Number of coins that Kimberly had at first
= 112 - 60
= 52

Answer(s): 52