Three containers, A, B and C, contained 189 marbles. Jack added some marbles into Container A and the number of marbles in Container A tripled. He took out half of the number of marbles from Container B and added another 51 marbles into Container C. As a result, the ratio of the number of marbles in Container A, Container B and Container C became 12 : 3 : 5. What was the ratio of the number of marbles in Container B to the total number of marbles in Container A and Container C at first? Give the answer in its lowest term.

	Container A	Container B	Container C	Total
Before	1x4 = 4 u	2x3 = 6 u	5 u - 51	189
Change	+ 2x4 = + 8 u	- 1x3 = - 3 u	+ 51
After	3x4 = 12 u	1x3 = 3 u
Comparing the 3 containers	12 u	3 u	5 u

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

The number of marbles in Container B in the end is repeated. Make the number of marbles in Container B in the end the same. LCM of 1 and 3 is 3.

Total number of marbles at first
= 4 u + 6 u + 5 u - 51
= 15 u - 51

15 u - 51 = 189
15 u = 189 + 51
15 u = 240

1 u = 240 ÷ 15 = 16

Number of marbles in Container B at first
= 6 u
= 6 x 16
= 96

Number of marbles in Container A and Container C at first
= 189 - 96
= 93

Container B : Container A and Container C
96 : 93 _(÷3)
32 : 31

Answer(s): 32 : 31