Three containers, C, A and B, contained 188 marbles. Bobby 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 20 marbles into Container B. As a result, the ratio of the number of marbles in Container C, Container A and Container B became 9 : 3 : 7. 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 |
2x3 =
6 u |
7 u - 20 |
188 |
| Change |
+ 2x3 =
+ 6 u |
- 1x3 =
- 3 u |
+ 20 |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
|
|
Comparing the
3 containers |
9 u |
3 u |
7 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 3 is 3.
Total number of marbles at first
= 3 u + 6 u + 7 u - 20
= 16 u - 20
16 u - 20 = 188
16 u = 188 + 20
16 u = 208
1 u = 208 ÷ 16 = 13
Number of marbles in Container A at first
= 6 u
= 6 x 13
= 78
Number of marbles in Container C and Container B at first
= 188 - 78
= 110
Container A : Container C and Container B
78 : 110
(÷2)39 : 55
Answer(s): 39 : 55
