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

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

Number of erasers that Gem and Yen each had in the end is the same.

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

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

7 p = 21

1 p = 21 ÷ 7 = 3

Number of erasers that Yen had after receiving some erasers from Gem
= 8 p
= 8 x 3
= 24

Number of erasers that Gem had after giving to Yen
= 42 - 24
= 18

3 u = 18

1 u = 18 ÷ 3 = 6

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

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

Answer(s): 18