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

	Xuan	Shannon	Total
Before 1	?	4 u	30
Change 1	+ 1 u	- 1 u
After 1	18	3 u	30
Before 2	6 p	3 u	30
Change 2	- 1 p	+ 1 p
After 2	5 p (15)	15	30

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

Number of coins that Shannon and Xuan each had in the end is the same.

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

Number of coins that Xuan had in the end = 5 p

5 p = 15

1 p = 15 ÷ 5 = 3

Number of coins that Xuan had after receiving some coins from Shannon
= 6 p
= 6 x 3
= 18

Number of coins that Shannon had after giving to Xuan
= 30 - 18
= 12

3 u = 12

1 u = 12 ÷ 3 = 4

Number of coins that Shannon had at first
= 4 u
= 4 x 4
= 16

Number of coins that Xuan had at first
= 30 - 16
= 14

Answer(s): 14