Three containers, C, A and B, contained 238 marbles. Sam 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 28 marbles into Container B. As a result, the ratio of the number of marbles in Container C, Container A and Container B became 9 : 4 : 3. 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 |
1x3 = 3 u |
2x4 = 8 u |
3 u - 28 |
238 |
Change |
+ 2x3 = + 6 u |
- 1x4 = - 4 u |
+ 28 |
|
After |
3x3 = 9 u |
1x4 = 4 u |
|
|
Comparing the 3 containers |
9 u |
4 u |
3 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 9 is 9.
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 4 is 4.
Total number of marbles at first
= 3 u + 8 u + 3 u - 28
= 14 u - 28
14 u - 28 = 238
14 u = 238 + 28
14 u = 266
1 u = 266 ÷ 14 = 19
Number of marbles in Container A at first
= 8 u
= 8 x 19
= 152
Number of marbles in Container C and Container B at first
= 238 - 152
= 86
Container A : Container C and Container B
152 : 86
(÷2)76 : 43
Answer(s): 76 : 43