Esther and Marion had a total of 120 pens. Marion gave ¹₄ of her pens to Esther. In return, Esther gave ¹₆ of the total number of pens that she had to Marion. In the end, each girl had the same number of pens. How many pens did Esther have at first?

	Esther	Marion	Total
Before 1	?	4 u	120
Change 1	+ 1 u	- 1 u
After 1	72	3 u	120
Before 2	6 p	3 u	120
Change 2	- 1 p	+ 1 p
After 2	5 p (60)	60	120

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

Number of pens that Marion and Esther each had in the end is the same.

Number of pens that Esther had in the end
= 120 ÷ 2
= 60

Number of pens that Esther had in the end = 5 p

5 p = 60

1 p = 60 ÷ 5 = 12

Number of pens that Esther had after receiving some pens from Marion
= 6 p
= 6 x 12
= 72

Number of pens that Marion had after giving to Esther
= 120 - 72
= 48

3 u = 48

1 u = 48 ÷ 3 = 16

Number of pens that Marion had at first
= 4 u
= 4 x 16
= 64

Number of pens that Esther had at first
= 120 - 64
= 56

Answer(s): 56