Linda and Betty had a total of 48 pens. Betty gave ¹₃ of her pens to Linda. In return, Linda gave ¹₇ of the total number of pens that she had to Betty. In the end, each girl had the same number of pens. How many pens did Linda have at first?

	Linda	Betty	Total
Before 1	?	3 u	48
Change 1	+ 1 u	- 1 u
After 1	28	2 u	48
Before 2	7 p	2 u	48
Change 2	- 1 p	+ 1 p
After 2	6 p (24)	24	48

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

Number of pens that Betty and Linda each had in the end is the same.

Number of pens that Linda had in the end
= 48 ÷ 2
= 24

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

6 p = 24

1 p = 24 ÷ 6 = 4

Number of pens that Linda had after receiving some pens from Betty
= 7 p
= 7 x 4
= 28

Number of pens that Betty had after giving to Linda
= 48 - 28
= 20

2 u = 20

1 u = 20 ÷ 2 = 10

Number of pens that Betty had at first
= 3 u
= 3 x 10
= 30

Number of pens that Linda had at first
= 48 - 30
= 18

Answer(s): 18