Three containers, B, C and A, contained 306 beads. Brandon 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 36 beads from Container A. As a result, the ratio of the number of beads in Container B, Container C and Container A became 9 : 2 : 11. 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 |
1x3 =
3 u |
2x2 =
4 u |
11 u + 36 |
306 |
| Change |
+ 2x3 =
+ 6 u |
- 1x2 =
- 2 u |
- 36 |
|
| After |
3x3 =
9 u |
1x2 =
2 u |
|
|
Comparing the
3 containers |
9 u
|
2 u |
11 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 9 is 9.
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
= 3 u + 4 u + 11 u + 36
= 18 u + 36
18 u + 36 = 306
18 u = 306 - 36
18 u = 270
1 u = 270 ÷ 18 = 15
Number of beads in Container A at first
= 11 u + 36
= 11 x 15 + 36
= 165 + 36
= 201
Number of beads in Container B and Container C at first
= 306 - 201
= 105
Container A : Container B and Container C
201 : 105
(÷3)67 : 35
Answer(s): 67 : 35
