Mark had ¹₂ as many beads as Fabian. Fabian had ²₃ as many beads as Jaslyn. After Mark and Jaslyn gave 18 beads to Fabian, Fabian had four times as many beads as Mark. Jaslyn then had the same number of beads as Fabian.

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

Mark	Fabian	Jaslyn
1	2
	2	3
1	2	3

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

Ratio of the number of beads that Jaslyn had to the number of beads that Mark had in the beginning = 3 : 1

	Mark	Fabian	Jaslyn	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 18	+ 36	- 18
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 Mark and Jaslyn
= 2 x 18
= 36

Number of beads that Fabian received from Mark and Jaslyn
= 2 x 1 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

Number of beads that Ashley had in the end
= 8 u
= 8 x 9
= 72