Abi and Zoe had a total of 40 erasers. Zoe gave ¹₃ of her erasers to Abi. In return, Abi gave ¹₆ of the total number of erasers that she had to Zoe. In the end, each girl had the same number of erasers. How many erasers did Abi have at first?

	Abi	Zoe	Total
Before 1	?	3 u	40
Change 1	+ 1 u	- 1 u
After 1	24	2 u	40
Before 2	6 p	2 u	40
Change 2	- 1 p	+ 1 p
After 2	5 p (20)	20	40

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

Number of erasers that Zoe and Abi each had in the end is the same.

Number of erasers that Abi had in the end
= 40 ÷ 2
= 20

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

5 p = 20

1 p = 20 ÷ 5 = 4

Number of erasers that Abi had after receiving some erasers from Zoe
= 6 p
= 6 x 4
= 24

Number of erasers that Zoe had after giving to Abi
= 40 - 24
= 16

2 u = 16

1 u = 16 ÷ 2 = 8

Number of erasers that Zoe had at first
= 3 u
= 3 x 8
= 24

Number of erasers that Abi had at first
= 40 - 24
= 16

Answer(s): 16