Three containers, A, B and C, contained 220 beads. Asher 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 27 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 : 5. 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 |
5 u - 27 |
220 |
Change |
+ 2x4 = + 8 u |
- 1x2 = - 2 u |
+ 27 |
|
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 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 + 5 u - 27
= 13 u - 27
13 u - 27 = 220
13 u = 220 + 27
13 u = 247
1 u = 247 ÷ 13 = 19
Number of beads in Container B at first
= 4 u
= 4 x 19
= 76
Number of beads in Container A and Container C at first
= 220 - 76
= 144
Container B : Container A and Container C
76 : 144
(÷4)19 : 36
Answer(s): 19 : 36