Nick had ¹₂ as many marbles as Mark. Mark had ²₃ as many marbles as Risa. After Nick and Risa gave 18 marbles to Mark, Mark had four times as many marbles as Nick. Risa then had the same number of marbles as Mark.

1. What was the ratio of the number of marbles Nick had to the number of marbles Risa had in the beginning? Answer in simplest form.
2. How many marbles did Mark have in the end?

Nick	Mark	Risa
1	2
	2	3
1	2	3

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

Ratio of the number of marbles that Nick had to the number of marbles that Risa had in the beginning = 1 : 3

	Nick	Mark	Risa	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 Mark received from Nick and Risa
= 2 x 18
= 36

Number of marbles that Mark received from Nick and Risa
= 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