Kathy and Esther had a total of 140 stickers. Esther gave ¹₃ of her stickers to Kathy. In return, Kathy gave ¹₈ of the total number of stickers that she had to Esther. In the end, each girl had the same number of stickers. How many stickers did Kathy have at first?

	Kathy	Esther	Total
Before 1	?	3 u	140
Change 1	+ 1 u	- 1 u
After 1	80	2 u	140
Before 2	8 p	2 u	140
Change 2	- 1 p	+ 1 p
After 2	7 p (70)	70	140

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

Number of stickers that Esther and Kathy each had in the end is the same.

Number of stickers that Kathy had in the end
= 140 ÷ 2
= 70

Number of stickers that Kathy had in the end = 7 p

7 p = 70

1 p = 70 ÷ 7 = 10

Number of stickers that Kathy had after receiving some stickers from Esther
= 8 p
= 8 x 10
= 80

Number of stickers that Esther had after giving to Kathy
= 140 - 80
= 60

2 u = 60

1 u = 60 ÷ 2 = 30

Number of stickers that Esther had at first
= 3 u
= 3 x 30
= 90

Number of stickers that Kathy had at first
= 140 - 90
= 50

Answer(s): 50