Jane and Emily had a total of 98 erasers. Emily gave ¹₄ of her erasers to Jane. In return, Jane gave ¹₈ of the total number of erasers that she had to Emily. In the end, each girl had the same number of erasers. How many erasers did Jane have at first?

	Jane	Emily	Total
Before 1	?	4 u	98
Change 1	+ 1 u	- 1 u
After 1	56	3 u	98
Before 2	8 p	3 u	98
Change 2	- 1 p	+ 1 p
After 2	7 p (49)	49	98

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

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

Number of erasers that Jane had in the end
= 98 ÷ 2
= 49

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

7 p = 49

1 p = 49 ÷ 7 = 7

Number of erasers that Jane had after receiving some erasers from Emily
= 8 p
= 8 x 7
= 56

Number of erasers that Emily had after giving to Jane
= 98 - 56
= 42

3 u = 42

1 u = 42 ÷ 3 = 14

Number of erasers that Emily had at first
= 4 u
= 4 x 14
= 56

Number of erasers that Jane had at first
= 98 - 56
= 42

Answer(s): 42