Three cartons, C, A and B, contained 270 marbles. Glen added some marbles into Carton C and the number of marbles in Carton C tripled. He took out half of the number of marbles from Carton A and added another 30 marbles into Carton B. As a result, the ratio of the number of marbles in Carton C, Carton A and Carton B became 12 : 4 : 3. What was the ratio of the number of marbles in Carton A to the total number of marbles in Carton C and Carton B at first? Give the answer in its lowest term.

	Carton C	Carton A	Carton B	Total
Before	1x4 = 4 u	2x4 = 8 u	3 u - 30	270
Change	+ 2x4 = + 8 u	- 1x4 = - 4 u	+ 30
After	3x4 = 12 u	1x4 = 4 u
Comparing the 3 cartons	12 u	4 u	3 u

The number of marbles in Carton C in the end is repeated.  Make the number of marbles in Carton C in the end the same. LCM of 3 and 12 is 12.

The number of marbles in Carton A in the end is repeated. Make the number of marbles in Carton A in the end the same. LCM of 1 and 4 is 4.

Total number of marbles at first
= 4 u + 8 u + 3 u - 30
= 15 u - 30

15 u - 30 = 270
15 u = 270 + 30
15 u = 300

1 u = 300 ÷ 15 = 20

Number of marbles in Carton A at first
= 8 u
= 8 x 20
= 160

Number of marbles in Carton C and Carton B at first
= 270 - 160
= 110

Carton A : Carton C and Carton B
160 : 110 _(÷10)
16 : 11

Answer(s): 16 : 11