Zara and Winnie had a total of 48 marbles. Winnie gave ¹₃ of her marbles to Zara. In return, Zara gave ¹₅ of the total number of marbles that she had to Winnie. In the end, each girl had the same number of marbles. How many marbles did Zara have at first?

	Zara	Winnie	Total
Before 1	?	3 u	48
Change 1	+ 1 u	- 1 u
After 1	30	2 u	48
Before 2	5 p	2 u	48
Change 2	- 1 p	+ 1 p
After 2	4 p (24)	24	48

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

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

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

Number of marbles that Zara had in the end = 4 p

4 p = 24

1 p = 24 ÷ 4 = 6

Number of marbles that Zara had after receiving some marbles from Winnie
= 5 p
= 5 x 6
= 30

Number of marbles that Winnie had after giving to Zara
= 48 - 30
= 18

2 u = 18

1 u = 18 ÷ 2 = 9

Number of marbles that Winnie had at first
= 3 u
= 3 x 9
= 27

Number of marbles that Zara had at first
= 48 - 27
= 21

Answer(s): 21