Three containers, B, C and A, contained 180 beads. Nick 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 11 beads from Container A. As a result, the ratio of the number of beads in Container B, Container C and Container A became 6 : 2 : 7. 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 |
1x2 = 2 u |
2x2 = 4 u |
7 u + 11 |
180 |
Change |
+ 2x2 = + 4 u |
- 1x2 = - 2 u |
- 11 |
|
After |
3x2 = 6 u |
1x2 = 2 u |
|
|
Comparing the 3 containers |
6 u
|
2 u |
7 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 6 is 6.
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
= 2 u + 4 u + 7 u + 11
= 13 u + 11
13 u + 11 = 180
13 u = 180 - 11
13 u = 169
1 u = 169 ÷ 13 = 13
Number of beads in Container A at first
= 7 u + 11
= 7 x 13 + 11
= 91 + 11
= 102
Number of beads in Container B and Container C at first
= 180 - 102
= 78
Container A : Container B and Container C
102 : 78
(÷6)17 : 13
Answer(s): 17 : 13