Three containers, B, C and A, contained 291 beads. Ryan added some beads into Container B and the number of beads in Container B tripled. He took out half of the number of beads from Container C and added another 70 beads into Container A. As a result, the ratio of the number of beads in Container B, Container C and Container A became 6 : 3 : 11. What was the ratio of the number of beads in Container C to the total number of beads in Container B and Container A at first? Give the answer in its lowest term.
| |
Container B |
Container C |
Container A |
Total |
| Before |
1x2 =
2 u |
2x3 =
6 u |
11 u - 70 |
291 |
| Change |
+ 2x2 =
+ 4 u |
- 1x3 =
- 3 u |
+ 70 |
|
| After |
3x2 =
6 u |
1x3 =
3 u |
|
|
Comparing the
3 containers |
6 u |
3 u |
11 u |
|
The number of beads in Container B in the end is repeated. Make the number of beads in Container B in the end the same. LCM of 3 and 6 is 6.
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 1 and 3 is 3.
Total number of beads at first
= 2 u + 6 u + 11 u - 70
= 19 u - 70
19 u - 70 = 291
19 u = 291 + 70
19 u = 361
1 u = 361 ÷ 19 = 19
Number of beads in Container C at first
= 6 u
= 6 x 19
= 114
Number of beads in Container B and Container A at first
= 291 - 114
= 177
Container C : Container B and Container A
114 : 177
(÷3)38 : 59
Answer(s): 38 : 59
