Flynn had ³₄ as many beads as Simon. Simon had ⁴₇ as many beads as Vanessa. After Flynn and Vanessa gave 6 beads to Simon, Simon had thrice as many beads as Flynn. Vanessa then had the same number of beads as Simon.

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

Flynn	Simon	Vanessa
3	4
	4	7
3	4	7

(a)
The number of beads that Simon is repeated.  

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

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

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

Number of beads that Simon received from Flynn and Vanessa
= 2 x 6
= 12

Number of beads that Simon received from Flynn and Vanessa
= 2 x 1 u
= 2 u

2 u = 6

1 u = 6 ÷ 2 = 3

Number of beads that Ashley had in the end
= 6 u
= 6 x 3
= 18