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

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

Number of coins that Yen and Lucy each had in the end is the same.

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

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

7 p = 70

1 p = 70 ÷ 7 = 10

Number of coins that Lucy had after receiving some coins from Yen
= 8 p
= 8 x 10
= 80

Number of coins that Yen had after giving to Lucy
= 140 - 80
= 60

5 u = 60

1 u = 60 ÷ 5 = 12

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

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

Answer(s): 68