Three containers, C, A and B, contained 156 marbles. Valen added some marbles into Container C and the number of marbles in Container C tripled. He took out half of the number of marbles from Container A and added another 39 marbles into Container B. As a result, the ratio of the number of marbles in Container C, Container A and Container B became 12 : 2 : 5. What was the ratio of the number of marbles in Container A to the total number of marbles in Container C and Container B at first? Give the answer in its lowest term.
| |
Container C |
Container A |
Container B |
Total |
| Before |
1x4 =
4 u |
2x2 =
4 u |
5 u - 39 |
156 |
| Change |
+ 2x4 =
+ 8 u |
- 1x2 =
- 2 u |
+ 39 |
|
| After |
3x4 =
12 u |
1x2 =
2 u |
|
|
Comparing the
3 containers |
12 u |
2 u |
5 u |
|
The number of marbles in Container C in the end is repeated. Make the number of marbles in Container C in the end the same. LCM of 3 and 12 is 12.
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 1 and 2 is 2.
Total number of marbles at first
= 4 u + 4 u + 5 u - 39
= 13 u - 39
13 u - 39 = 156
13 u = 156 + 39
13 u = 195
1 u = 195 ÷ 13 = 15
Number of marbles in Container A at first
= 4 u
= 4 x 15
= 60
Number of marbles in Container C and Container B at first
= 156 - 60
= 96
Container A : Container C and Container B
60 : 96
(÷12)5 : 8
Answer(s): 5 : 8
