Victoria and Penelope had a total of 110 erasers. Penelope gave ¹₃ of her erasers to Victoria. In return, Victoria gave ¹₆ of the total number of erasers that she had to Penelope. In the end, each girl had the same number of erasers. How many erasers did Victoria have at first?

	Victoria	Penelope	Total
Before 1	?	3 u	110
Change 1	+ 1 u	- 1 u
After 1	66	2 u	110
Before 2	6 p	2 u	110
Change 2	- 1 p	+ 1 p
After 2	5 p (55)	55	110

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

Number of erasers that Penelope and Victoria each had in the end is the same.

Number of erasers that Victoria had in the end
= 110 ÷ 2
= 55

Number of erasers that Victoria had in the end = 5 p

5 p = 55

1 p = 55 ÷ 5 = 11

Number of erasers that Victoria had after receiving some erasers from Penelope
= 6 p
= 6 x 11
= 66

Number of erasers that Penelope had after giving to Victoria
= 110 - 66
= 44

2 u = 44

1 u = 44 ÷ 2 = 22

Number of erasers that Penelope had at first
= 3 u
= 3 x 22
= 66

Number of erasers that Victoria had at first
= 110 - 66
= 44

Answer(s): 44