Olivia and Nora had a total of 48 marbles. Nora gave ¹₅ of her marbles to Olivia. In return, Olivia gave ¹₇ of the total number of marbles that she had to Nora. In the end, each girl had the same number of marbles. How many marbles did Olivia have at first?

	Olivia	Nora	Total
Before 1	?	5 u	48
Change 1	+ 1 u	- 1 u
After 1	28	4 u	48
Before 2	7 p	4 u	48
Change 2	- 1 p	+ 1 p
After 2	6 p (24)	24	48

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

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

Number of marbles that Olivia had in the end
= 48 ÷ 2
= 24

Number of marbles that Olivia had in the end = 6 p

6 p = 24

1 p = 24 ÷ 6 = 4

Number of marbles that Olivia had after receiving some marbles from Nora
= 7 p
= 7 x 4
= 28

Number of marbles that Nora had after giving to Olivia
= 48 - 28
= 20

4 u = 20

1 u = 20 ÷ 4 = 5

Number of marbles that Nora had at first
= 5 u
= 5 x 5
= 25

Number of marbles that Olivia had at first
= 48 - 25
= 23

Answer(s): 23