Esther and Olivia had a total of 144 stamps. Olivia gave ¹₅ of her stamps to Esther. In return, Esther gave ¹₇ of the total number of stamps that she had to Olivia. In the end, each girl had the same number of stamps. How many stamps did Esther have at first?

	Esther	Olivia	Total
Before 1	?	5 u	144
Change 1	+ 1 u	- 1 u
After 1	84	4 u	144
Before 2	7 p	4 u	144
Change 2	- 1 p	+ 1 p
After 2	6 p (72)	72	144

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

Number of stamps that Olivia and Esther each had in the end is the same.

Number of stamps that Esther had in the end
= 144 ÷ 2
= 72

Number of stamps that Esther had in the end = 6 p

6 p = 72

1 p = 72 ÷ 6 = 12

Number of stamps that Esther had after receiving some stamps from Olivia
= 7 p
= 7 x 12
= 84

Number of stamps that Olivia had after giving to Esther
= 144 - 84
= 60

4 u = 60

1 u = 60 ÷ 4 = 15

Number of stamps that Olivia had at first
= 5 u
= 5 x 15
= 75

Number of stamps that Esther had at first
= 144 - 75
= 69

Answer(s): 69