Glen had ¹₂ as many marbles as Peter. Peter had ²₃ as many marbles as Barbara. After Glen and Barbara gave 12 marbles to Peter, Peter had four times as many marbles as Glen. Barbara then had the same number of marbles as Peter.

1. What was the ratio of the number of marbles Glen had to the number of marbles Barbara had in the beginning? Answer in simplest form.
2. How many marbles did Peter have in the end?

Glen	Peter	Barbara
1	2
	2	3
1	2	3

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

Ratio of the number of marbles that Glen had to the number of marbles that Barbara had in the beginning = 1 : 3

	Glen	Peter	Barbara	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 Peter received from Glen and Barbara
= 2 x 12
= 24

Number of marbles that Peter received from Glen and Barbara
= 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