Lucy and Risa had a total of 96 coins. Risa gave ¹₃ of her coins to Lucy. In return, Lucy gave ¹₇ of the total number of coins that she had to Risa. In the end, each girl had the same number of coins. How many coins did Lucy have at first?

	Lucy	Risa	Total
Before 1	?	3 u	96
Change 1	+ 1 u	- 1 u
After 1	56	2 u	96
Before 2	7 p	2 u	96
Change 2	- 1 p	+ 1 p
After 2	6 p (48)	48	96

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

Number of coins that Risa and Lucy each had in the end is the same.

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

Number of coins that Lucy had in the end = 6 p

6 p = 48

1 p = 48 ÷ 6 = 8

Number of coins that Lucy had after receiving some coins from Risa
= 7 p
= 7 x 8
= 56

Number of coins that Risa had after giving to Lucy
= 96 - 56
= 40

2 u = 40

1 u = 40 ÷ 2 = 20

Number of coins that Risa had at first
= 3 u
= 3 x 20
= 60

Number of coins that Lucy had at first
= 96 - 60
= 36

Answer(s): 36