Emily and Tina had a total of 42 erasers. Tina gave ¹₄ of her erasers to Emily. In return, Emily gave ¹₈ of the total number of erasers that she had to Tina. In the end, each girl had the same number of erasers. How many erasers did Emily have at first?

	Emily	Tina	Total
Before 1	?	4 u	42
Change 1	+ 1 u	- 1 u
After 1	24	3 u	42
Before 2	8 p	3 u	42
Change 2	- 1 p	+ 1 p
After 2	7 p (21)	21	42

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

Number of erasers that Tina and Emily each had in the end is the same.

Number of erasers that Emily had in the end
= 42 ÷ 2
= 21

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

7 p = 21

1 p = 21 ÷ 7 = 3

Number of erasers that Emily had after receiving some erasers from Tina
= 8 p
= 8 x 3
= 24

Number of erasers that Tina had after giving to Emily
= 42 - 24
= 18

3 u = 18

1 u = 18 ÷ 3 = 6

Number of erasers that Tina had at first
= 4 u
= 4 x 6
= 24

Number of erasers that Emily had at first
= 42 - 24
= 18

Answer(s): 18