Jen and Hazel had a total of 126 stamps. Hazel gave ¹₄ of her stamps to Jen. In return, Jen gave ¹₈ of the total number of stamps that she had to Hazel. In the end, each girl had the same number of stamps. How many stamps did Jen have at first?

	Jen	Hazel	Total
Before 1	?	4 u	126
Change 1	+ 1 u	- 1 u
After 1	72	3 u	126
Before 2	8 p	3 u	126
Change 2	- 1 p	+ 1 p
After 2	7 p (63)	63	126

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

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

Number of stamps that Jen had in the end
= 126 ÷ 2
= 63

Number of stamps that Jen had in the end = 7 p

7 p = 63

1 p = 63 ÷ 7 = 9

Number of stamps that Jen had after receiving some stamps from Hazel
= 8 p
= 8 x 9
= 72

Number of stamps that Hazel had after giving to Jen
= 126 - 72
= 54

3 u = 54

1 u = 54 ÷ 3 = 18

Number of stamps that Hazel had at first
= 4 u
= 4 x 18
= 72

Number of stamps that Jen had at first
= 126 - 72
= 54

Answer(s): 54