Barbara and Anna had a total of 126 erasers. Anna gave ¹₄ of her erasers to Barbara. In return, Barbara gave ¹₈ 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 Barbara have at first?

	Barbara	Anna	Total
Before 1	?	4 u	126
Change 1	+ 1 u	- 1 u
After 1	72	3 u	126
Before 2	8 p	3 u	126
Change 2	- 1 p	+ 1 p
After 2	7 p (63)	63	126

Since Anna gave some erasers to Barbara and Barbara 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 Barbara each had in the end is the same.

Number of erasers that Barbara had in the end
= 126 ÷ 2
= 63

Number of erasers that Barbara had in the end = 7 p

7 p = 63

1 p = 63 ÷ 7 = 9

Number of erasers that Barbara had after receiving some erasers from Anna
= 8 p
= 8 x 9
= 72

Number of erasers that Anna had after giving to Barbara
= 126 - 72
= 54

3 u = 54

1 u = 54 ÷ 3 = 18

Number of erasers that Anna had at first
= 4 u
= 4 x 18
= 72

Number of erasers that Barbara had at first
= 126 - 72
= 54

Answer(s): 54