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

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

Number of erasers that Natalie and Pamela each had in the end is the same.

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

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

5 p = 55

1 p = 55 ÷ 5 = 11

Number of erasers that Pamela had after receiving some erasers from Natalie
= 6 p
= 6 x 11
= 66

Number of erasers that Natalie had after giving to Pamela
= 110 - 66
= 44

2 u = 44

1 u = 44 ÷ 2 = 22

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

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

Answer(s): 44