Fanny and Abi had a total of 60 marbles. Abi gave ¹₃ of her marbles to Fanny. In return, Fanny gave ¹₆ of the total number of marbles that she had to Abi. In the end, each girl had the same number of marbles. How many marbles did Fanny have at first?

	Fanny	Abi	Total
Before 1	?	3 u	60
Change 1	+ 1 u	- 1 u
After 1	36	2 u	60
Before 2	6 p	2 u	60
Change 2	- 1 p	+ 1 p
After 2	5 p (30)	30	60

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

Number of marbles that Abi and Fanny each had in the end is the same.

Number of marbles that Fanny had in the end
= 60 ÷ 2
= 30

Number of marbles that Fanny had in the end = 5 p

5 p = 30

1 p = 30 ÷ 5 = 6

Number of marbles that Fanny had after receiving some marbles from Abi
= 6 p
= 6 x 6
= 36

Number of marbles that Abi had after giving to Fanny
= 60 - 36
= 24

2 u = 24

1 u = 24 ÷ 2 = 12

Number of marbles that Abi had at first
= 3 u
= 3 x 12
= 36

Number of marbles that Fanny had at first
= 60 - 36
= 24

Answer(s): 24