Three containers, A, B and C, contained 238 beads. Jack 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 58 beads from Container C. As a result, the ratio of the number of beads in Container A, Container B and Container C became 6 : 4 : 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 |
1x2 = 2 u |
2x4 = 8 u |
5 u + 58 |
238 |
Change |
+ 2x2 = + 4 u |
- 1x4 = - 4 u |
- 58 |
|
After |
3x2 = 6 u |
1x4 = 4 u |
|
|
Comparing the 3 containers |
6 u
|
4 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 6 is 6.
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 4 is 4.
Total number of beads at first
= 2 u + 8 u + 5 u + 58
= 15 u + 58
15 u + 58 = 238
15 u = 238 - 58
15 u = 180
1 u = 180 ÷ 15 = 12
Number of beads in Container C at first
= 5 u + 58
= 5 x 12 + 58
= 60 + 58
= 118
Number of beads in Container A and Container B at first
= 238 - 118
= 120
Container C : Container A and Container B
118 : 120
(÷2)59 : 60
Answer(s): 59 : 60