Joelle and Raeann had a total of 56 pens. Raeann gave ¹₄ of her pens to Joelle. In return, Joelle gave ¹₈ of the total number of pens that she had to Raeann. In the end, each girl had the same number of pens. How many pens did Joelle have at first?

	Joelle	Raeann	Total
Before 1	?	4 u	56
Change 1	+ 1 u	- 1 u
After 1	32	3 u	56
Before 2	8 p	3 u	56
Change 2	- 1 p	+ 1 p
After 2	7 p (28)	28	56

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

Number of pens that Raeann and Joelle each had in the end is the same.

Number of pens that Joelle had in the end
= 56 ÷ 2
= 28

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

7 p = 28

1 p = 28 ÷ 7 = 4

Number of pens that Joelle had after receiving some pens from Raeann
= 8 p
= 8 x 4
= 32

Number of pens that Raeann had after giving to Joelle
= 56 - 32
= 24

3 u = 24

1 u = 24 ÷ 3 = 8

Number of pens that Raeann had at first
= 4 u
= 4 x 8
= 32

Number of pens that Joelle had at first
= 56 - 32
= 24

Answer(s): 24