Shiyun and Winnie had a total of 30 pens. Winnie gave ¹₆ of her pens to Shiyun. In return, Shiyun gave ¹₄ of the total number of pens that she had to Winnie. In the end, each girl had the same number of pens. How many pens did Shiyun have at first?

	Shiyun	Winnie	Total
Before 1	?	6 u	30
Change 1	+ 1 u	- 1 u
After 1	20	5 u	30
Before 2	4 p	5 u	30
Change 2	- 1 p	+ 1 p
After 2	3 p (15)	15	30

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

Number of pens that Winnie and Shiyun each had in the end is the same.

Number of pens that Shiyun had in the end
= 30 ÷ 2
= 15

Number of pens that Shiyun had in the end = 3 p

3 p = 15

1 p = 15 ÷ 3 = 5

Number of pens that Shiyun had after receiving some pens from Winnie
= 4 p
= 4 x 5
= 20

Number of pens that Winnie had after giving to Shiyun
= 30 - 20
= 10

5 u = 10

1 u = 10 ÷ 5 = 2

Number of pens that Winnie had at first
= 6 u
= 6 x 2
= 12

Number of pens that Shiyun had at first
= 30 - 12
= 18

Answer(s): 18