Tommy had ¹₂ as many marbles as Oscar. Oscar had ²₃ as many marbles as Min. After Tommy and Min gave 12 marbles to Oscar, Oscar had four times as many marbles as Tommy. Min then had the same number of marbles as Oscar.

1. What was the ratio of the number of marbles Tommy had to the number of marbles Min had in the beginning? Answer in simplest form.
2. How many marbles did Oscar have in the end?

Tommy	Oscar	Min
1	2
	2	3
1	2	3

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

Ratio of the number of marbles that Tommy had to the number of marbles that Min had in the beginning = 1 : 3

	Tommy	Oscar	Min	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 12	+ 24	- 12
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 Oscar received from Tommy and Min
= 2 x 12
= 24

Number of marbles that Oscar received from Tommy and Min
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

Number of marbles that Ashley had in the end
= 8 u
= 8 x 6
= 48