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

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

Number of pens that Kathy and Barbara each had in the end is the same.

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

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

6 p = 72

1 p = 72 ÷ 6 = 12

Number of pens that Barbara had after receiving some pens from Kathy
= 7 p
= 7 x 12
= 84

Number of pens that Kathy had after giving to Barbara
= 144 - 84
= 60

4 u = 60

1 u = 60 ÷ 4 = 15

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

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

Answer(s): 69