Gabby and Irene had a total of 70 stamps. Irene gave ¹₃ of her stamps to Gabby. In return, Gabby gave ¹₆ of the total number of stamps that she had to Irene. In the end, each girl had the same number of stamps. How many stamps did Gabby have at first?

	Gabby	Irene	Total
Before 1	?	3 u	70
Change 1	+ 1 u	- 1 u
After 1	42	2 u	70
Before 2	6 p	2 u	70
Change 2	- 1 p	+ 1 p
After 2	5 p (35)	35	70

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

Number of stamps that Irene and Gabby each had in the end is the same.

Number of stamps that Gabby had in the end
= 70 ÷ 2
= 35

Number of stamps that Gabby had in the end = 5 p

5 p = 35

1 p = 35 ÷ 5 = 7

Number of stamps that Gabby had after receiving some stamps from Irene
= 6 p
= 6 x 7
= 42

Number of stamps that Irene had after giving to Gabby
= 70 - 42
= 28

2 u = 28

1 u = 28 ÷ 2 = 14

Number of stamps that Irene had at first
= 3 u
= 3 x 14
= 42

Number of stamps that Gabby had at first
= 70 - 42
= 28

Answer(s): 28