Jen and Emma had a total of 80 stamps. Emma gave ¹₆ of her stamps to Jen. In return, Jen gave ¹₅ of the total number of stamps that she had to Emma. In the end, each girl had the same number of stamps. How many stamps did Jen have at first?

	Jen	Emma	Total
Before 1	?	6 u	80
Change 1	+ 1 u	- 1 u
After 1	50	5 u	80
Before 2	5 p	5 u	80
Change 2	- 1 p	+ 1 p
After 2	4 p (40)	40	80

Since Emma gave some stamps to Jen and Jen then gave some stamps to Emma, it is an internal transfer of stamps between the two girls. So, the total number of stamps remains unchanged.

Number of stamps that Emma and Jen each had in the end is the same.

Number of stamps that Jen had in the end
= 80 ÷ 2
= 40

Number of stamps that Jen had in the end = 4 p

4 p = 40

1 p = 40 ÷ 4 = 10

Number of stamps that Jen had after receiving some stamps from Emma
= 5 p
= 5 x 10
= 50

Number of stamps that Emma had after giving to Jen
= 80 - 50
= 30

5 u = 30

1 u = 30 ÷ 5 = 6

Number of stamps that Emma had at first
= 6 u
= 6 x 6
= 36

Number of stamps that Jen had at first
= 80 - 36
= 44

Answer(s): 44