Flynn had ³₄ as many cards as Xavier. Xavier had ⁴₇ as many cards as Vanessa. After Flynn and Vanessa gave 12 cards to Xavier, Xavier had thrice as many cards as Flynn. Vanessa then had the same number of cards as Xavier.

1. What was the ratio of the number of cards Flynn had to the number of cards Vanessa had in the beginning? Answer in simplest form.
2. How many cards did Xavier have in the end?

Flynn	Xavier	Vanessa
3	4
	4	7
3	4	7

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

Ratio of the number of cards that Flynn had to the number of cards that Vanessa had in the beginning = 3 : 7

	Flynn	Xavier	Vanessa	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 12	+ 24	- 12
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of cards at first and in the end remains unchanged. Make the total number of cards the same. LCM of 14 and 7 is 14.

Number of cards that Xavier received from Flynn and Vanessa
= 2 x 12
= 24

Number of cards that Xavier received from Flynn and Vanessa
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

Number of cards that Ashley had in the end
= 6 u
= 6 x 6
= 36