Mary and Fiona had a total of 168 pens. Fiona gave ¹₅ of her pens to Mary. In return, Mary gave ¹₈ of the total number of pens that she had to Fiona. In the end, each girl had the same number of pens. How many pens did Mary have at first?

	Mary	Fiona	Total
Before 1	?	5 u	168
Change 1	+ 1 u	- 1 u
After 1	96	4 u	168
Before 2	8 p	4 u	168
Change 2	- 1 p	+ 1 p
After 2	7 p (84)	84	168

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

Number of pens that Fiona and Mary each had in the end is the same.

Number of pens that Mary had in the end
= 168 ÷ 2
= 84

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

7 p = 84

1 p = 84 ÷ 7 = 12

Number of pens that Mary had after receiving some pens from Fiona
= 8 p
= 8 x 12
= 96

Number of pens that Fiona had after giving to Mary
= 168 - 96
= 72

4 u = 72

1 u = 72 ÷ 4 = 18

Number of pens that Fiona had at first
= 5 u
= 5 x 18
= 90

Number of pens that Mary had at first
= 168 - 90
= 78

Answer(s): 78