Roshel and Esther had a total of 84 pens. Esther gave ¹₄ of her pens to Roshel. In return, Roshel gave ¹₈ of the total number of pens that she had to Esther. In the end, each girl had the same number of pens. How many pens did Roshel have at first?

	Roshel	Esther	Total
Before 1	?	4 u	84
Change 1	+ 1 u	- 1 u
After 1	48	3 u	84
Before 2	8 p	3 u	84
Change 2	- 1 p	+ 1 p
After 2	7 p (42)	42	84

Since Esther gave some pens to Roshel and Roshel then gave some pens to Esther, it is an internal transfer of pens between the two girls. So, the total number of pens remains unchanged.

Number of pens that Esther and Roshel each had in the end is the same.

Number of pens that Roshel had in the end
= 84 ÷ 2
= 42

Number of pens that Roshel had in the end = 7 p

7 p = 42

1 p = 42 ÷ 7 = 6

Number of pens that Roshel had after receiving some pens from Esther
= 8 p
= 8 x 6
= 48

Number of pens that Esther had after giving to Roshel
= 84 - 48
= 36

3 u = 36

1 u = 36 ÷ 3 = 12

Number of pens that Esther had at first
= 4 u
= 4 x 12
= 48

Number of pens that Roshel had at first
= 84 - 48
= 36

Answer(s): 36