Vincent had ¹₂ as many beads as Fabian. Fabian had ²₃ as many beads as Winnie. After Vincent and Winnie gave 14 beads to Fabian, Fabian had four times as many beads as Vincent. Winnie then had the same number of beads as Fabian.

1. What was the ratio of the number of beads Winnie had to the number of beads Vincent had in the beginning? Answer in simplest form.
2. How many beads did Fabian have in the end?

Vincent	Fabian	Winnie
1	2
	2	3
1	2	3

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

Ratio of the number of beads that Winnie had to the number of beads that Vincent had in the beginning = 3 : 1

	Vincent	Fabian	Winnie	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 beads at first and in the end remains unchanged. Make the total number of beads the same. LCM of 6 and 9 is 18.

Number of beads that Fabian received from Vincent and Winnie
= 2 x 14
= 28

Number of beads that Fabian received from Vincent and Winnie
= 2 x 1 u
= 2 u

2 u = 14

1 u = 14 ÷ 2 = 7

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