Will had ¹₂ as many cards as Sean. Sean had ²₃ as many cards as Fiona. After Will and Fiona gave 14 cards to Sean, Sean had four times as many cards as Will. Fiona then had the same number of cards as Sean.

1. What was the ratio of the number of cards Fiona had to the number of cards Will had in the beginning? Answer in simplest form.
2. How many cards did Sean have in the end?

Will	Sean	Fiona
1	2
	2	3
1	2	3

(a)
The number of cards that Sean is repeated.  

Ratio of the number of cards that Fiona had to the number of cards that Will had in the beginning = 3 : 1

	Will	Sean	Fiona	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 14	+ 28	- 14
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of cards at first and in the end remains unchanged. Make the total number of cards the same. LCM of 6 and 9 is 18.

Number of cards that Sean received from Will and Fiona
= 2 x 14
= 28

Number of cards that Sean received from Will and Fiona
= 2 x 1 u
= 2 u

2 u = 14

1 u = 14 ÷ 2 = 7

Number of cards that Ashley had in the end
= 8 u
= 8 x 7
= 56