Three containers, A, B and C, contained 180 marbles. Albert 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 92 marbles into Container C. As a result, the ratio of the number of marbles in Container A, Container B and Container C became 9 : 2 : 9. 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 |
1x3 = 3 u |
2x2 = 4 u |
9 u - 92 |
180 |
Change |
+ 2x3 = + 6 u |
- 1x2 = - 2 u |
+ 92 |
|
After |
3x3 = 9 u |
1x2 = 2 u |
|
|
Comparing the 3 containers |
9 u |
2 u |
9 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 9 is 9.
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 2 is 2.
Total number of marbles at first
= 3 u + 4 u + 9 u - 92
= 16 u - 92
16 u - 92 = 180
16 u = 180 + 92
16 u = 272
1 u = 272 ÷ 16 = 17
Number of marbles in Container B at first
= 4 u
= 4 x 17
= 68
Number of marbles in Container A and Container C at first
= 180 - 68
= 112
Container B : Container A and Container C
68 : 112
(÷4)17 : 28
Answer(s): 17 : 28