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

	Mary	Tiffany	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 Tiffany gave some erasers to Mary and Mary then gave some erasers to Tiffany, it is an internal transfer of erasers between the two girls. So, the total number of erasers remains unchanged.

Number of erasers that Tiffany and Mary each had in the end is the same.

Number of erasers that Mary had in the end
= 120 ÷ 2
= 60

Number of erasers that Mary had in the end = 6 p

6 p = 60

1 p = 60 ÷ 6 = 10

Number of erasers that Mary had after receiving some erasers from Tiffany
= 7 p
= 7 x 10
= 70

Number of erasers that Tiffany had after giving to Mary
= 120 - 70
= 50

2 u = 50

1 u = 50 ÷ 2 = 25

Number of erasers that Tiffany had at first
= 3 u
= 3 x 25
= 75

Number of erasers that Mary had at first
= 120 - 75
= 45

Answer(s): 45