Three containers, B, C and A, contained 246 beads. Eric 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 removed 25 beads from Container A. As a result, the ratio of the number of beads in Container B, Container C and Container A became 12 : 2 : 5. What was the ratio of the number of beads in Container A to the total number of beads in Container B and Container C at first? Give the answer in its lowest term.
|
Container B |
Container C |
Container A |
Total |
Before |
1x4 = 4 u |
2x2 = 4 u |
5 u + 25 |
246 |
Change |
+ 2x4 = + 8 u |
- 1x2 = - 2 u |
- 25 |
|
After |
3x4 = 12 u |
1x2 = 2 u |
|
|
Comparing the 3 containers |
12 u
|
2 u |
5 u |
|
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 3 and 12 is 12.
The number of beads in Container C in the end is the same. Make the number of beads in Container C in the end the same. LCM of 1 and 2 is 2.
Total number of beads at first
= 4 u + 4 u + 5 u + 25
= 13 u + 25
13 u + 25 = 246
13 u = 246 - 25
13 u = 221
1 u = 221 ÷ 13 = 17
Number of beads in Container A at first
= 5 u + 25
= 5 x 17 + 25
= 85 + 25
= 110
Number of beads in Container B and Container C at first
= 246 - 110
= 136
Container A : Container B and Container C
110 : 136
(÷2)55 : 68
Answer(s): 55 : 68