Three containers, C, A and B, contained 207 beads. Valen added some beads into Container C and the number of beads in Container C tripled. He took out half of the number of beads from Container A and added another 33 beads into Container B. As a result, the ratio of the number of beads in Container C, Container A and Container B became 9 : 2 : 9. What was the ratio of the number of beads in Container A to the total number of beads 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 |
2x2 =
4 u |
9 u - 33 |
207 |
| Change |
+ 2x3 =
+ 6 u |
- 1x2 =
- 2 u |
+ 33 |
|
| After |
3x3 =
9 u |
1x2 =
2 u |
|
|
Comparing the
3 containers |
9 u |
2 u |
9 u |
|
The number of beads in Container C in the end is repeated. Make the number of beads in Container C in the end the same. LCM of 3 and 9 is 9.
The number of beads in Container A in the end is repeated. Make the number of beads in Container A in the end the same. LCM of 1 and 2 is 2.
Total number of beads at first
= 3 u + 4 u + 9 u - 33
= 16 u - 33
16 u - 33 = 207
16 u = 207 + 33
16 u = 240
1 u = 240 ÷ 16 = 15
Number of beads in Container A at first
= 4 u
= 4 x 15
= 60
Number of beads in Container C and Container B at first
= 207 - 60
= 147
Container A : Container C and Container B
60 : 147
(÷3)20 : 49
Answer(s): 20 : 49
