Lucy and Vanessa had a total of 120 stamps. Vanessa gave ¹₃ of her stamps to Lucy. In return, Lucy gave ¹₇ of the total number of stamps that she had to Vanessa. In the end, each girl had the same number of stamps. How many stamps did Lucy have at first?

	Lucy	Vanessa	Total
Before 1	?	3 u	120
Change 1	+ 1 u	- 1 u
After 1	70	2 u	120
Before 2	7 p	2 u	120
Change 2	- 1 p	+ 1 p
After 2	6 p (60)	60	120

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

Number of stamps that Vanessa and Lucy each had in the end is the same.

Number of stamps that Lucy had in the end
= 120 ÷ 2
= 60

Number of stamps that Lucy had in the end = 6 p

6 p = 60

1 p = 60 ÷ 6 = 10

Number of stamps that Lucy had after receiving some stamps from Vanessa
= 7 p
= 7 x 10
= 70

Number of stamps that Vanessa had after giving to Lucy
= 120 - 70
= 50

2 u = 50

1 u = 50 ÷ 2 = 25

Number of stamps that Vanessa had at first
= 3 u
= 3 x 25
= 75

Number of stamps that Lucy had at first
= 120 - 75
= 45

Answer(s): 45