Owen had ¹₂ as many marbles as Will. Will had ²₃ as many marbles as Irene. After Owen and Irene gave 18 marbles to Will, Will had four times as many marbles as Owen. Irene then had the same number of marbles as Will.

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

Owen	Will	Irene
1	2
	2	3
1	2	3

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

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

	Owen	Will	Irene	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 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 Will received from Owen and Irene
= 2 x 18
= 36

Number of marbles that Will received from Owen and Irene
= 2 x 1 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

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