Three containers, A, B and C, contained 148 marbles. David 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 76 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 - 76 |
148 |
| Change |
+ 2x3 =
+ 6 u |
- 1x2 =
- 2 u |
+ 76 |
|
| 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 - 76
= 16 u - 76
16 u - 76 = 148
16 u = 148 + 76
16 u = 224
1 u = 224 ÷ 16 = 14
Number of marbles in Container B at first
= 4 u
= 4 x 14
= 56
Number of marbles in Container A and Container C at first
= 148 - 56
= 92
Container B : Container A and Container C
56 : 92
(÷4)14 : 23
Answer(s): 14 : 23
