Min and Hazel had a total of 30 coins. Hazel gave ¹₆ of her coins to Min. In return, Min gave ¹₄ of the total number of coins that she had to Hazel. In the end, each girl had the same number of coins. How many coins did Min have at first?

	Min	Hazel	Total
Before 1	?	6 u	30
Change 1	+ 1 u	- 1 u
After 1	20	5 u	30
Before 2	4 p	5 u	30
Change 2	- 1 p	+ 1 p
After 2	3 p (15)	15	30

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

Number of coins that Hazel and Min each had in the end is the same.

Number of coins that Min had in the end
= 30 ÷ 2
= 15

Number of coins that Min had in the end = 3 p

3 p = 15

1 p = 15 ÷ 3 = 5

Number of coins that Min had after receiving some coins from Hazel
= 4 p
= 4 x 5
= 20

Number of coins that Hazel had after giving to Min
= 30 - 20
= 10

5 u = 10

1 u = 10 ÷ 5 = 2

Number of coins that Hazel had at first
= 6 u
= 6 x 2
= 12

Number of coins that Min had at first
= 30 - 12
= 18

Answer(s): 18