Fanny and Diana had a total of 144 pens. Diana gave ¹₅ of her pens to Fanny. In return, Fanny gave ¹₇ of the total number of pens that she had to Diana. In the end, each girl had the same number of pens. How many pens did Fanny have at first?

	Fanny	Diana	Total
Before 1	?	5 u	144
Change 1	+ 1 u	- 1 u
After 1	84	4 u	144
Before 2	7 p	4 u	144
Change 2	- 1 p	+ 1 p
After 2	6 p (72)	72	144

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

Number of pens that Diana and Fanny each had in the end is the same.

Number of pens that Fanny had in the end
= 144 ÷ 2
= 72

Number of pens that Fanny had in the end = 6 p

6 p = 72

1 p = 72 ÷ 6 = 12

Number of pens that Fanny had after receiving some pens from Diana
= 7 p
= 7 x 12
= 84

Number of pens that Diana had after giving to Fanny
= 144 - 84
= 60

4 u = 60

1 u = 60 ÷ 4 = 15

Number of pens that Diana had at first
= 5 u
= 5 x 15
= 75

Number of pens that Fanny had at first
= 144 - 75
= 69

Answer(s): 69