Irene and Joelle had a total of 30 pens. Joelle gave ¹₆ of her pens to Irene. In return, Irene gave ¹₄ of the total number of pens that she had to Joelle. In the end, each girl had the same number of pens. How many pens did Irene have at first?

	Irene	Joelle	Total
Before 1	?	6 u	30
Change 1	+ 1 u	- 1 u
After 1	20	5 u	30
Before 2	4 p	5 u	30
Change 2	- 1 p	+ 1 p
After 2	3 p (15)	15	30

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

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

Number of pens that Irene had in the end
= 30 ÷ 2
= 15

Number of pens that Irene had in the end = 3 p

3 p = 15

1 p = 15 ÷ 3 = 5

Number of pens that Irene had after receiving some pens from Joelle
= 4 p
= 4 x 5
= 20

Number of pens that Joelle had after giving to Irene
= 30 - 20
= 10

5 u = 10

1 u = 10 ÷ 5 = 2

Number of pens that Joelle had at first
= 6 u
= 6 x 2
= 12

Number of pens that Irene had at first
= 30 - 12
= 18

Answer(s): 18