Hilda and Fiona had a total of 72 coins. Fiona gave ¹₄ of her coins to Hilda. In return, Hilda gave ¹₇ of the total number of coins that she had to Fiona. In the end, each girl had the same number of coins. How many coins did Hilda have at first?

	Hilda	Fiona	Total
Before 1	?	4 u	72
Change 1	+ 1 u	- 1 u
After 1	42	3 u	72
Before 2	7 p	3 u	72
Change 2	- 1 p	+ 1 p
After 2	6 p (36)	36	72

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

Number of coins that Fiona and Hilda each had in the end is the same.

Number of coins that Hilda had in the end
= 72 ÷ 2
= 36

Number of coins that Hilda had in the end = 6 p

6 p = 36

1 p = 36 ÷ 6 = 6

Number of coins that Hilda had after receiving some coins from Fiona
= 7 p
= 7 x 6
= 42

Number of coins that Fiona had after giving to Hilda
= 72 - 42
= 30

3 u = 30

1 u = 30 ÷ 3 = 10

Number of coins that Fiona had at first
= 4 u
= 4 x 10
= 40

Number of coins that Hilda had at first
= 72 - 40
= 32

Answer(s): 32