Xylia and Emily had a total of 126 pens. Emily gave ¹₄ of her pens to Xylia. In return, Xylia gave ¹₈ of the total number of pens that she had to Emily. In the end, each girl had the same number of pens. How many pens did Xylia have at first?

	Xylia	Emily	Total
Before 1	?	4 u	126
Change 1	+ 1 u	- 1 u
After 1	72	3 u	126
Before 2	8 p	3 u	126
Change 2	- 1 p	+ 1 p
After 2	7 p (63)	63	126

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

Number of pens that Emily and Xylia each had in the end is the same.

Number of pens that Xylia had in the end
= 126 ÷ 2
= 63

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

7 p = 63

1 p = 63 ÷ 7 = 9

Number of pens that Xylia had after receiving some pens from Emily
= 8 p
= 8 x 9
= 72

Number of pens that Emily had after giving to Xylia
= 126 - 72
= 54

3 u = 54

1 u = 54 ÷ 3 = 18

Number of pens that Emily had at first
= 4 u
= 4 x 18
= 72

Number of pens that Xylia had at first
= 126 - 72
= 54

Answer(s): 54