Three containers, A, B and C, contained 146 beads. Ethan 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 added another 63 beads into Container C. As a result, the ratio of the number of beads in Container A, Container B and Container C became 12 : 2 : 11. What was the ratio of the number of beads in Container B to the total number of beads in Container A and Container C at first? Give the answer in its lowest term.
|
Container A |
Container B |
Container C |
Total |
Before |
1x4 = 4 u |
2x2 = 4 u |
11 u - 63 |
146 |
Change |
+ 2x4 = + 8 u |
- 1x2 = - 2 u |
+ 63 |
|
After |
3x4 = 12 u |
1x2 = 2 u |
|
|
Comparing the 3 containers |
12 u |
2 u |
11 u |
|
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 3 and 12 is 12.
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 1 and 2 is 2.
Total number of beads at first
= 4 u + 4 u + 11 u - 63
= 19 u - 63
19 u - 63 = 146
19 u = 146 + 63
19 u = 209
1 u = 209 ÷ 19 = 11
Number of beads in Container B at first
= 4 u
= 4 x 11
= 44
Number of beads in Container A and Container C at first
= 146 - 44
= 102
Container B : Container A and Container C
44 : 102
(÷2)22 : 51
Answer(s): 22 : 51