Xylia and Elyse had a total of 84 stamps. Elyse gave ¹₅ of her stamps to Xylia. In return, Xylia gave ¹₈ of the total number of stamps that she had to Elyse. In the end, each girl had the same number of stamps. How many stamps did Xylia have at first?

	Xylia	Elyse	Total
Before 1	?	5 u	84
Change 1	+ 1 u	- 1 u
After 1	48	4 u	84
Before 2	8 p	4 u	84
Change 2	- 1 p	+ 1 p
After 2	7 p (42)	42	84

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

Number of stamps that Elyse and Xylia each had in the end is the same.

Number of stamps that Xylia had in the end
= 84 ÷ 2
= 42

Number of stamps that Xylia had in the end = 7 p

7 p = 42

1 p = 42 ÷ 7 = 6

Number of stamps that Xylia had after receiving some stamps from Elyse
= 8 p
= 8 x 6
= 48

Number of stamps that Elyse had after giving to Xylia
= 84 - 48
= 36

4 u = 36

1 u = 36 ÷ 4 = 9

Number of stamps that Elyse had at first
= 5 u
= 5 x 9
= 45

Number of stamps that Xylia had at first
= 84 - 45
= 39

Answer(s): 39