Three containers, A, B and C, contained 306 beads. Liam added some beads into Container A and the number of beads in Container A tripled. He took out half of the number of beads from Container B and removed 46 beads from Container C. As a result, the ratio of the number of beads in Container A, Container B and Container C became 12 : 2 : 5. What was the ratio of the number of beads in Container C to the total number of beads in Container A and Container B at first? Give the answer in its lowest term.
|
Container A |
Container B |
Container C |
Total |
Before |
1x4 = 4 u |
2x2 = 4 u |
5 u + 46 |
306 |
Change |
+ 2x4 = + 8 u |
- 1x2 = - 2 u |
- 46 |
|
After |
3x4 = 12 u |
1x2 = 2 u |
|
|
Comparing the 3 containers |
12 u
|
2 u |
5 u |
|
The number of beads in Container A in the end is the same. Make the number of beads in Container A in the end the same. LCM of 3 and 12 is 12.
The number of beads in Container B in the end is the same. Make the number of beads in Container B in the end the same. LCM of 1 and 2 is 2.
Total number of beads at first
= 4 u + 4 u + 5 u + 46
= 13 u + 46
13 u + 46 = 306
13 u = 306 - 46
13 u = 260
1 u = 260 ÷ 13 = 20
Number of beads in Container C at first
= 5 u + 46
= 5 x 20 + 46
= 100 + 46
= 146
Number of beads in Container A and Container B at first
= 306 - 146
= 160
Container C : Container A and Container B
146 : 160
(÷2)73 : 80
Answer(s): 73 : 80