Erika and Winnie had a total of 112 coins. Winnie gave ¹₃ of her coins to Erika. In return, Erika gave ¹₈ of the total number of coins that she had to Winnie. In the end, each girl had the same number of coins. How many coins did Erika have at first?

	Erika	Winnie	Total
Before 1	?	3 u	112
Change 1	+ 1 u	- 1 u
After 1	64	2 u	112
Before 2	8 p	2 u	112
Change 2	- 1 p	+ 1 p
After 2	7 p (56)	56	112

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

Number of coins that Winnie and Erika each had in the end is the same.

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

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

7 p = 56

1 p = 56 ÷ 7 = 8

Number of coins that Erika had after receiving some coins from Winnie
= 8 p
= 8 x 8
= 64

Number of coins that Winnie had after giving to Erika
= 112 - 64
= 48

2 u = 48

1 u = 48 ÷ 2 = 24

Number of coins that Winnie had at first
= 3 u
= 3 x 24
= 72

Number of coins that Erika had at first
= 112 - 72
= 40

Answer(s): 40