Sarah and Sabrina had a total of 80 stamps. Sabrina gave ¹₃ of her stamps to Sarah. In return, Sarah gave ¹₅ of the total number of stamps that she had to Sabrina. In the end, each girl had the same number of stamps. How many stamps did Sarah have at first?

	Sarah	Sabrina	Total
Before 1	?	3 u	80
Change 1	+ 1 u	- 1 u
After 1	50	2 u	80
Before 2	5 p	2 u	80
Change 2	- 1 p	+ 1 p
After 2	4 p (40)	40	80

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

Number of stamps that Sabrina and Sarah each had in the end is the same.

Number of stamps that Sarah had in the end
= 80 ÷ 2
= 40

Number of stamps that Sarah had in the end = 4 p

4 p = 40

1 p = 40 ÷ 4 = 10

Number of stamps that Sarah had after receiving some stamps from Sabrina
= 5 p
= 5 x 10
= 50

Number of stamps that Sabrina had after giving to Sarah
= 80 - 50
= 30

2 u = 30

1 u = 30 ÷ 2 = 15

Number of stamps that Sabrina had at first
= 3 u
= 3 x 15
= 45

Number of stamps that Sarah had at first
= 80 - 45
= 35

Answer(s): 35