Three cartons, A, B and C, contained 267 marbles. Asher 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 85 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 : 7. 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	7 u + 85	267
Change	+ 2x2 = + 4 u	- 1x2 = - 2 u	- 85
After	3x2 = 6 u	1x2 = 2 u
Comparing the 3 cartons	6 u	2 u	7 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 + 7 u + 85
= 13 u + 85

13 u + 85 = 267
13 u = 267 - 85
13 u = 182

1 u = 182 ÷ 13 = 14

Number of marbles in Carton C at first
= 7 u + 85
= 7 x 14 + 85
= 98 + 85
= 183

Number of marbles in Carton A and Carton B at first
= 267 - 183
= 84

Carton C : Carton A and Carton B
183 : 84 _(÷3)
61 : 28

Answer(s): 61 : 28