Wendy and Xuan had a total of 36 pens. Xuan gave ¹₅ of her pens to Wendy. In return, Wendy gave ¹₄ of the total number of pens that she had to Xuan. In the end, each girl had the same number of pens. How many pens did Wendy have at first?

	Wendy	Xuan	Total
Before 1	?	5 u	36
Change 1	+ 1 u	- 1 u
After 1	24	4 u	36
Before 2	4 p	4 u	36
Change 2	- 1 p	+ 1 p
After 2	3 p (18)	18	36

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

Number of pens that Xuan and Wendy each had in the end is the same.

Number of pens that Wendy had in the end
= 36 ÷ 2
= 18

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

3 p = 18

1 p = 18 ÷ 3 = 6

Number of pens that Wendy had after receiving some pens from Xuan
= 4 p
= 4 x 6
= 24

Number of pens that Xuan had after giving to Wendy
= 36 - 24
= 12

4 u = 12

1 u = 12 ÷ 4 = 3

Number of pens that Xuan had at first
= 5 u
= 5 x 3
= 15

Number of pens that Wendy had at first
= 36 - 15
= 21

Answer(s): 21