Nicole and Cathy had a total of 98 stickers. Cathy gave ¹₃ of her stickers to Nicole. In return, Nicole gave ¹₈ of the total number of stickers that she had to Cathy. In the end, each girl had the same number of stickers. How many stickers did Nicole have at first?

	Nicole	Cathy	Total
Before 1	?	3 u	98
Change 1	+ 1 u	- 1 u
After 1	56	2 u	98
Before 2	8 p	2 u	98
Change 2	- 1 p	+ 1 p
After 2	7 p (49)	49	98

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

Number of stickers that Cathy and Nicole each had in the end is the same.

Number of stickers that Nicole had in the end
= 98 ÷ 2
= 49

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

7 p = 49

1 p = 49 ÷ 7 = 7

Number of stickers that Nicole had after receiving some stickers from Cathy
= 8 p
= 8 x 7
= 56

Number of stickers that Cathy had after giving to Nicole
= 98 - 56
= 42

2 u = 42

1 u = 42 ÷ 2 = 21

Number of stickers that Cathy had at first
= 3 u
= 3 x 21
= 63

Number of stickers that Nicole had at first
= 98 - 63
= 35

Answer(s): 35