Owen had ¹₂ as many marbles as Jeremy. Jeremy had ²₃ as many marbles as Shannon. After Owen and Shannon gave 20 marbles to Jeremy, Jeremy had four times as many marbles as Owen. Shannon then had the same number of marbles as Jeremy.

1. What was the ratio of the number of marbles Owen had to the number of marbles Shannon had in the beginning? Answer in simplest form.
2. How many marbles did Jeremy have in the end?

Owen	Jeremy	Shannon
1	2
	2	3
1	2	3

(a)
The number of marbles that Jeremy is repeated.  

Ratio of the number of marbles that Owen had to the number of marbles that Shannon had in the beginning = 1 : 3

	Owen	Jeremy	Shannon	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 20	+ 40	- 20
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

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

Number of marbles that Jeremy received from Owen and Shannon
= 2 x 20
= 40

Number of marbles that Jeremy received from Owen and Shannon
= 2 x 1 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

Number of marbles that Ashley had in the end
= 8 u
= 8 x 10
= 80