Victoria and Ivory had a total of 90 stamps. Ivory gave ¹₃ of her stamps to Victoria. In return, Victoria gave ¹₆ of the total number of stamps that she had to Ivory. In the end, each girl had the same number of stamps. How many stamps did Victoria have at first?

	Victoria	Ivory	Total
Before 1	?	3 u	90
Change 1	+ 1 u	- 1 u
After 1	54	2 u	90
Before 2	6 p	2 u	90
Change 2	- 1 p	+ 1 p
After 2	5 p (45)	45	90

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

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

Number of stamps that Victoria had in the end
= 90 ÷ 2
= 45

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

5 p = 45

1 p = 45 ÷ 5 = 9

Number of stamps that Victoria had after receiving some stamps from Ivory
= 6 p
= 6 x 9
= 54

Number of stamps that Ivory had after giving to Victoria
= 90 - 54
= 36

2 u = 36

1 u = 36 ÷ 2 = 18

Number of stamps that Ivory had at first
= 3 u
= 3 x 18
= 54

Number of stamps that Victoria had at first
= 90 - 54
= 36

Answer(s): 36