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

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

Number of stamps that Zoe and Victoria each had in the end is the same.

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

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

4 p = 40

1 p = 40 ÷ 4 = 10

Number of stamps that Victoria had after receiving some stamps from Zoe
= 5 p
= 5 x 10
= 50

Number of stamps that Zoe had after giving to Victoria
= 80 - 50
= 30

2 u = 30

1 u = 30 ÷ 2 = 15

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

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

Answer(s): 35