Three containers, C, A and B, contained 160 beads. Japheth added some beads into Container C and the number of beads in Container C tripled. He took out half of the number of beads from Container A and added another 11 beads into Container B. As a result, the ratio of the number of beads in Container C, Container A and Container B became 6 : 2 : 3. What was the ratio of the number of beads in Container A to the total number of beads in Container C and Container B at first? Give the answer in its lowest term.
| |
Container C |
Container A |
Container B |
Total |
| Before |
1x2 =
2 u |
2x2 =
4 u |
3 u - 11 |
160 |
| Change |
+ 2x2 =
+ 4 u |
- 1x2 =
- 2 u |
+ 11 |
|
| After |
3x2 =
6 u |
1x2 =
2 u |
|
|
Comparing the
3 containers |
6 u |
2 u |
3 u |
|
The number of beads in Container C in the end is repeated. Make the number of beads in Container C in the end the same. LCM of 3 and 6 is 6.
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 1 and 2 is 2.
Total number of beads at first
= 2 u + 4 u + 3 u - 11
= 9 u - 11
9 u - 11 = 160
9 u = 160 + 11
9 u = 171
1 u = 171 ÷ 9 = 19
Number of beads in Container A at first
= 4 u
= 4 x 19
= 76
Number of beads in Container C and Container B at first
= 160 - 76
= 84
Container A : Container C and Container B
76 : 84
(÷4)19 : 21
Answer(s): 19 : 21
