Zoe and Yoko had a total of 16 pens. Yoko gave ¹₃ of her pens to Zoe. In return, Zoe gave ¹₅ of the total number of pens that she had to Yoko. In the end, each girl had the same number of pens. How many pens did Zoe have at first?

	Zoe	Yoko	Total
Before 1	?	3 u	16
Change 1	+ 1 u	- 1 u
After 1	10	2 u	16
Before 2	5 p	2 u	16
Change 2	- 1 p	+ 1 p
After 2	4 p (8)	8	16

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

Number of pens that Yoko and Zoe each had in the end is the same.

Number of pens that Zoe had in the end
= 16 ÷ 2
= 8

Number of pens that Zoe had in the end = 4 p

4 p = 8

1 p = 8 ÷ 4 = 2

Number of pens that Zoe had after receiving some pens from Yoko
= 5 p
= 5 x 2
= 10

Number of pens that Yoko had after giving to Zoe
= 16 - 10
= 6

2 u = 6

1 u = 6 ÷ 2 = 3

Number of pens that Yoko had at first
= 3 u
= 3 x 3
= 9

Number of pens that Zoe had at first
= 16 - 9
= 7

Answer(s): 7