Emily and Kylie had a total of 56 coins. Kylie gave ¹₄ of her coins to Emily. In return, Emily gave ¹₈ of the total number of coins that she had to Kylie. In the end, each girl had the same number of coins. How many coins did Emily have at first?

	Emily	Kylie	Total
Before 1	?	4 u	56
Change 1	+ 1 u	- 1 u
After 1	32	3 u	56
Before 2	8 p	3 u	56
Change 2	- 1 p	+ 1 p
After 2	7 p (28)	28	56

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

Number of coins that Kylie and Emily each had in the end is the same.

Number of coins that Emily had in the end
= 56 ÷ 2
= 28

Number of coins that Emily had in the end = 7 p

7 p = 28

1 p = 28 ÷ 7 = 4

Number of coins that Emily had after receiving some coins from Kylie
= 8 p
= 8 x 4
= 32

Number of coins that Kylie had after giving to Emily
= 56 - 32
= 24

3 u = 24

1 u = 24 ÷ 3 = 8

Number of coins that Kylie had at first
= 4 u
= 4 x 8
= 32

Number of coins that Emily had at first
= 56 - 32
= 24

Answer(s): 24