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

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

Number of marbles that Zoe and Penelope each had in the end is the same.

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

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

7 p = 70

1 p = 70 ÷ 7 = 10

Number of marbles that Penelope had after receiving some marbles from Zoe
= 8 p
= 8 x 10
= 80

Number of marbles that Zoe had after giving to Penelope
= 140 - 80
= 60

5 u = 60

1 u = 60 ÷ 5 = 12

Number of marbles that Zoe had at first
= 6 u
= 6 x 12
= 72

Number of marbles that Penelope had at first
= 140 - 72
= 68

Answer(s): 68