Lucy and Anna had a total of 48 erasers. Anna gave ¹₃ of her erasers to Lucy. In return, Lucy gave ¹₇ of the total number of erasers that she had to Anna. In the end, each girl had the same number of erasers. How many erasers did Lucy have at first?

	Lucy	Anna	Total
Before 1	?	3 u	48
Change 1	+ 1 u	- 1 u
After 1	28	2 u	48
Before 2	7 p	2 u	48
Change 2	- 1 p	+ 1 p
After 2	6 p (24)	24	48

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

Number of erasers that Anna and Lucy each had in the end is the same.

Number of erasers that Lucy had in the end
= 48 ÷ 2
= 24

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

6 p = 24

1 p = 24 ÷ 6 = 4

Number of erasers that Lucy had after receiving some erasers from Anna
= 7 p
= 7 x 4
= 28

Number of erasers that Anna had after giving to Lucy
= 48 - 28
= 20

2 u = 20

1 u = 20 ÷ 2 = 10

Number of erasers that Anna had at first
= 3 u
= 3 x 10
= 30

Number of erasers that Lucy had at first
= 48 - 30
= 18

Answer(s): 18