Shiyun and Risa had a total of 168 coins. Risa gave ¹₃ of her coins to Shiyun. In return, Shiyun gave ¹₈ 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 Shiyun have at first?

	Shiyun	Risa	Total
Before 1	?	3 u	168
Change 1	+ 1 u	- 1 u
After 1	96	2 u	168
Before 2	8 p	2 u	168
Change 2	- 1 p	+ 1 p
After 2	7 p (84)	84	168

Since Risa gave some coins to Shiyun and Shiyun 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 Shiyun each had in the end is the same.

Number of coins that Shiyun had in the end
= 168 ÷ 2
= 84

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

7 p = 84

1 p = 84 ÷ 7 = 12

Number of coins that Shiyun had after receiving some coins from Risa
= 8 p
= 8 x 12
= 96

Number of coins that Risa had after giving to Shiyun
= 168 - 96
= 72

2 u = 72

1 u = 72 ÷ 2 = 36

Number of coins that Risa had at first
= 3 u
= 3 x 36
= 108

Number of coins that Shiyun had at first
= 168 - 108
= 60

Answer(s): 60