Lucy and Emily had a total of 140 marbles. Emily gave ¹₅ of her marbles to Lucy. In return, Lucy gave ¹₈ of the total number of marbles that she had to Emily. In the end, each girl had the same number of marbles. How many marbles did Lucy have at first?

	Lucy	Emily	Total
Before 1	?	5 u	140
Change 1	+ 1 u	- 1 u
After 1	80	4 u	140
Before 2	8 p	4 u	140
Change 2	- 1 p	+ 1 p
After 2	7 p (70)	70	140

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

Number of marbles that Emily and Lucy each had in the end is the same.

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

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

7 p = 70

1 p = 70 ÷ 7 = 10

Number of marbles that Lucy had after receiving some marbles from Emily
= 8 p
= 8 x 10
= 80

Number of marbles that Emily had after giving to Lucy
= 140 - 80
= 60

4 u = 60

1 u = 60 ÷ 4 = 15

Number of marbles that Emily had at first
= 5 u
= 5 x 15
= 75

Number of marbles that Lucy had at first
= 140 - 75
= 65

Answer(s): 65