Olivia and Zara had a total of 140 marbles. Zara gave ¹₃ of her marbles to Olivia. In return, Olivia gave ¹₈ of the total number of marbles that she had to Zara. In the end, each girl had the same number of marbles. How many marbles did Olivia have at first?

	Olivia	Zara	Total
Before 1	?	3 u	140
Change 1	+ 1 u	- 1 u
After 1	80	2 u	140
Before 2	8 p	2 u	140
Change 2	- 1 p	+ 1 p
After 2	7 p (70)	70	140

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

Number of marbles that Zara and Olivia each had in the end is the same.

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

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

7 p = 70

1 p = 70 ÷ 7 = 10

Number of marbles that Olivia had after receiving some marbles from Zara
= 8 p
= 8 x 10
= 80

Number of marbles that Zara had after giving to Olivia
= 140 - 80
= 60

2 u = 60

1 u = 60 ÷ 2 = 30

Number of marbles that Zara had at first
= 3 u
= 3 x 30
= 90

Number of marbles that Olivia had at first
= 140 - 90
= 50

Answer(s): 50