Rachel and Jade had a total of 70 erasers. Jade gave ¹₃ of her erasers to Rachel. In return, Rachel gave ¹₆ of the total number of erasers that she had to Jade. In the end, each girl had the same number of erasers. How many erasers did Rachel have at first?

	Rachel	Jade	Total
Before 1	?	3 u	70
Change 1	+ 1 u	- 1 u
After 1	42	2 u	70
Before 2	6 p	2 u	70
Change 2	- 1 p	+ 1 p
After 2	5 p (35)	35	70

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

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

Number of erasers that Rachel had in the end
= 70 ÷ 2
= 35

Number of erasers that Rachel had in the end = 5 p

5 p = 35

1 p = 35 ÷ 5 = 7

Number of erasers that Rachel had after receiving some erasers from Jade
= 6 p
= 6 x 7
= 42

Number of erasers that Jade had after giving to Rachel
= 70 - 42
= 28

2 u = 28

1 u = 28 ÷ 2 = 14

Number of erasers that Jade had at first
= 3 u
= 3 x 14
= 42

Number of erasers that Rachel had at first
= 70 - 42
= 28

Answer(s): 28