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

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

Number of erasers that Risa and Xuan each had in the end is the same.

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

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

6 p = 60

1 p = 60 ÷ 6 = 10

Number of erasers that Xuan had after receiving some erasers from Risa
= 7 p
= 7 x 10
= 70

Number of erasers that Risa had after giving to Xuan
= 120 - 70
= 50

2 u = 50

1 u = 50 ÷ 2 = 25

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

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

Answer(s): 45