Hazel and Vanessa had a total of 60 marbles. Vanessa gave ¹₄ of her marbles to Hazel. In return, Hazel gave ¹₆ of the total number of marbles that she had to Vanessa. In the end, each girl had the same number of marbles. How many marbles did Hazel have at first?

	Hazel	Vanessa	Total
Before 1	?	4 u	60
Change 1	+ 1 u	- 1 u
After 1	36	3 u	60
Before 2	6 p	3 u	60
Change 2	- 1 p	+ 1 p
After 2	5 p (30)	30	60

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

Number of marbles that Vanessa and Hazel each had in the end is the same.

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

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

5 p = 30

1 p = 30 ÷ 5 = 6

Number of marbles that Hazel had after receiving some marbles from Vanessa
= 6 p
= 6 x 6
= 36

Number of marbles that Vanessa had after giving to Hazel
= 60 - 36
= 24

3 u = 24

1 u = 24 ÷ 3 = 8

Number of marbles that Vanessa had at first
= 4 u
= 4 x 8
= 32

Number of marbles that Hazel had at first
= 60 - 32
= 28

Answer(s): 28