Nicole and Dana had a total of 140 coins. Dana gave ¹₆ of her coins to Nicole. In return, Nicole gave ¹₈ of the total number of coins that she had to Dana. In the end, each girl had the same number of coins. How many coins did Nicole have at first?

	Nicole	Dana	Total
Before 1	?	6 u	140
Change 1	+ 1 u	- 1 u
After 1	80	5 u	140
Before 2	8 p	5 u	140
Change 2	- 1 p	+ 1 p
After 2	7 p (70)	70	140

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

Number of coins that Dana and Nicole each had in the end is the same.

Number of coins that Nicole had in the end
= 140 ÷ 2
= 70

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

7 p = 70

1 p = 70 ÷ 7 = 10

Number of coins that Nicole had after receiving some coins from Dana
= 8 p
= 8 x 10
= 80

Number of coins that Dana had after giving to Nicole
= 140 - 80
= 60

5 u = 60

1 u = 60 ÷ 5 = 12

Number of coins that Dana had at first
= 6 u
= 6 x 12
= 72

Number of coins that Nicole had at first
= 140 - 72
= 68

Answer(s): 68