Jade and Dana had a total of 84 erasers. Dana gave ¹₅ of her erasers to Jade. In return, Jade gave ¹₈ of the total number of erasers that she had to Dana. In the end, each girl had the same number of erasers. How many erasers did Jade have at first?

	Jade	Dana	Total
Before 1	?	5 u	84
Change 1	+ 1 u	- 1 u
After 1	48	4 u	84
Before 2	8 p	4 u	84
Change 2	- 1 p	+ 1 p
After 2	7 p (42)	42	84

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

Number of erasers that Dana and Jade each had in the end is the same.

Number of erasers that Jade had in the end
= 84 ÷ 2
= 42

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

7 p = 42

1 p = 42 ÷ 7 = 6

Number of erasers that Jade had after receiving some erasers from Dana
= 8 p
= 8 x 6
= 48

Number of erasers that Dana had after giving to Jade
= 84 - 48
= 36

4 u = 36

1 u = 36 ÷ 4 = 9

Number of erasers that Dana had at first
= 5 u
= 5 x 9
= 45

Number of erasers that Jade had at first
= 84 - 45
= 39

Answer(s): 39