Three containers, A, B and C, contained 344 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 added another 16 beads into Container C. As a result, the ratio of the number of beads in Container A, Container B and Container C became 9 : 2 : 11. What was the ratio of the number of beads in Container B to the total number of beads in Container A and Container C at first? Give the answer in its lowest term.
| |
Container A |
Container B |
Container C |
Total |
| Before |
1x3 =
3 u |
2x2 =
4 u |
11 u - 16 |
344 |
| Change |
+ 2x3 =
+ 6 u |
- 1x2 =
- 2 u |
+ 16 |
|
| After |
3x3 =
9 u |
1x2 =
2 u |
|
|
Comparing the
3 containers |
9 u |
2 u |
11 u |
|
The number of beads in Container A in the end is repeated. Make the number of beads in Container A in the end the same. LCM of 3 and 9 is 9.
The number of beads in Container B in the end is repeated. Make the number of beads in Container B in the end the same. LCM of 1 and 2 is 2.
Total number of beads at first
= 3 u + 4 u + 11 u - 16
= 18 u - 16
18 u - 16 = 344
18 u = 344 + 16
18 u = 360
1 u = 360 ÷ 18 = 20
Number of beads in Container B at first
= 4 u
= 4 x 20
= 80
Number of beads in Container A and Container C at first
= 344 - 80
= 264
Container B : Container A and Container C
80 : 264
(÷8)10 : 33
Answer(s): 10 : 33
