Three containers, C, A and B, contained 476 marbles. Vaidev 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 removed 96 marbles from Container B. As a result, the ratio of the number of marbles in Container C, Container A and Container B became 6 : 4 : 9. What was the ratio of the number of marbles in Container B to the total number of marbles in Container C and Container A at first? Give the answer in its lowest term.
| |
Container C |
Container A |
Container B |
Total |
| Before |
1x2 =
2 u |
2x4 =
8 u |
9 u + 96 |
476 |
| Change |
+ 2x2 =
+ 4 u |
- 1x4 =
- 4 u |
- 96 |
|
| After |
3x2 =
6 u |
1x4 =
4 u |
|
|
Comparing the
3 containers |
6 u
|
4 u |
9 u |
|
The number of marbles in Container C in the end is the same. Make the number of marbles in Container C in the end the same. LCM of 3 and 6 is 6.
The number of marbles in Container A in the end is the same. 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
= 2 u + 8 u + 9 u + 96
= 19 u + 96
19 u + 96 = 476
19 u = 476 - 96
19 u = 380
1 u = 380 ÷ 19 = 20
Number of marbles in Container B at first
= 9 u + 96
= 9 x 20 + 96
= 180 + 96
= 276
Number of marbles in Container C and Container A at first
= 476 - 276
= 200
Container B : Container C and Container A
276 : 200
(÷4)69 : 50
Answer(s): 69 : 50
