Penelope and Shannon had a total of 32 stamps. Shannon gave ¹₅ of her stamps to Penelope. In return, Penelope gave ¹₃ of the total number of stamps that she had to Shannon. In the end, each girl had the same number of stamps. How many stamps did Penelope have at first?

	Penelope	Shannon	Total
Before 1	?	5 u	32
Change 1	+ 1 u	- 1 u
After 1	24	4 u	32
Before 2	3 p	4 u	32
Change 2	- 1 p	+ 1 p
After 2	2 p (16)	16	32

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

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

Number of stamps that Penelope had in the end
= 32 ÷ 2
= 16

Number of stamps that Penelope had in the end = 2 p

2 p = 16

1 p = 16 ÷ 2 = 8

Number of stamps that Penelope had after receiving some stamps from Shannon
= 3 p
= 3 x 8
= 24

Number of stamps that Shannon had after giving to Penelope
= 32 - 24
= 8

4 u = 8

1 u = 8 ÷ 4 = 2

Number of stamps that Shannon had at first
= 5 u
= 5 x 2
= 10

Number of stamps that Penelope had at first
= 32 - 10
= 22

Answer(s): 22