Shiyun and Penelope had a total of 110 stamps. Penelope gave ¹₃ of her stamps to Shiyun. In return, Shiyun gave ¹₆ of the total number of stamps that she had to Penelope. In the end, each girl had the same number of stamps. How many stamps did Shiyun have at first?

	Shiyun	Penelope	Total
Before 1	?	3 u	110
Change 1	+ 1 u	- 1 u
After 1	66	2 u	110
Before 2	6 p	2 u	110
Change 2	- 1 p	+ 1 p
After 2	5 p (55)	55	110

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

Number of stamps that Penelope and Shiyun each had in the end is the same.

Number of stamps that Shiyun had in the end
= 110 ÷ 2
= 55

Number of stamps that Shiyun had in the end = 5 p

5 p = 55

1 p = 55 ÷ 5 = 11

Number of stamps that Shiyun had after receiving some stamps from Penelope
= 6 p
= 6 x 11
= 66

Number of stamps that Penelope had after giving to Shiyun
= 110 - 66
= 44

2 u = 44

1 u = 44 ÷ 2 = 22

Number of stamps that Penelope had at first
= 3 u
= 3 x 22
= 66

Number of stamps that Shiyun had at first
= 110 - 66
= 44

Answer(s): 44