Three containers, A, B and C, contained 346 beads. Henry 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 91 beads from Container C. As a result, the ratio of the number of beads in Container A, Container B and Container C became 12 : 3 : 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 |
2x3 = 6 u |
5 u + 91 |
346 |
Change |
+ 2x4 = + 8 u |
- 1x3 = - 3 u |
- 91 |
|
After |
3x4 = 12 u |
1x3 = 3 u |
|
|
Comparing the 3 containers |
12 u
|
3 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 3 is 3.
Total number of beads at first
= 4 u + 6 u + 5 u + 91
= 15 u + 91
15 u + 91 = 346
15 u = 346 - 91
15 u = 255
1 u = 255 ÷ 15 = 17
Number of beads in Container C at first
= 5 u + 91
= 5 x 17 + 91
= 85 + 91
= 176
Number of beads in Container A and Container B at first
= 346 - 176
= 170
Container C : Container A and Container B
176 : 170
(÷2)88 : 85
Answer(s): 88 : 85