Three cartons, A, B and C, contained 326 marbles. Eric added some marbles into Carton A and the number of marbles in Carton A tripled. He took out half of the number of marbles from Carton B and removed 26 marbles from Carton C. As a result, the ratio of the number of marbles in Carton A, Carton B and Carton C became 6 : 2 : 9. What was the ratio of the number of marbles in Carton C to the total number of marbles in Carton A and Carton B at first? Give the answer in its lowest term.

	Carton A	Carton B	Carton C	Total
Before	1x2 = 2 u	2x2 = 4 u	9 u + 26	326
Change	+ 2x2 = + 4 u	- 1x2 = - 2 u	- 26
After	3x2 = 6 u	1x2 = 2 u
Comparing the 3 cartons	6 u	2 u	9 u

The number of marbles in Carton A in the end is the same. Make the number of marbles in Carton A in the end the same. LCM of 3 and 6 is 6.

The number of marbles in Carton B in the end is the same. Make the number of marbles in Carton B in the end the same. LCM of 1 and 2 is 2.

Total number of marbles at first
= 2 u + 4 u + 9 u + 26
= 15 u + 26

15 u + 26 = 326
15 u = 326 - 26
15 u = 300

1 u = 300 ÷ 15 = 20

Number of marbles in Carton C at first
= 9 u + 26
= 9 x 20 + 26
= 180 + 26
= 206

Number of marbles in Carton A and Carton B at first
= 326 - 206
= 120

Carton C : Carton A and Carton B
206 : 120 _(÷2)
103 : 60

Answer(s): 103 : 60