Xuan and Abi had a total of 168 erasers. Abi gave ¹₄ of her erasers to Xuan. In return, Xuan gave ¹₈ of the total number of erasers that she had to Abi. In the end, each girl had the same number of erasers. How many erasers did Xuan have at first?

	Xuan	Abi	Total
Before 1	?	4 u	168
Change 1	+ 1 u	- 1 u
After 1	96	3 u	168
Before 2	8 p	3 u	168
Change 2	- 1 p	+ 1 p
After 2	7 p (84)	84	168

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

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

Number of erasers that Xuan had in the end
= 168 ÷ 2
= 84

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

7 p = 84

1 p = 84 ÷ 7 = 12

Number of erasers that Xuan had after receiving some erasers from Abi
= 8 p
= 8 x 12
= 96

Number of erasers that Abi had after giving to Xuan
= 168 - 96
= 72

3 u = 72

1 u = 72 ÷ 3 = 24

Number of erasers that Abi had at first
= 4 u
= 4 x 24
= 96

Number of erasers that Xuan had at first
= 168 - 96
= 72

Answer(s): 72