Three containers, C, A and B, contained 195 beads. Will 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 removed 19 beads from Container B. As a result, the ratio of the number of beads in Container C, Container A and Container B became 9 : 3 : 7. What was the ratio of the number of beads in Container B to the total number of beads in Container C and Container A at first? Give the answer in its lowest term.
| |
Container C |
Container A |
Container B |
Total |
| Before |
1x3 =
3 u |
2x3 =
6 u |
7 u + 19 |
195 |
| Change |
+ 2x3 =
+ 6 u |
- 1x3 =
- 3 u |
- 19 |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
|
|
Comparing the
3 containers |
9 u
|
3 u |
7 u |
|
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 3 and 9 is 9.
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 1 and 3 is 3.
Total number of beads at first
= 3 u + 6 u + 7 u + 19
= 16 u + 19
16 u + 19 = 195
16 u = 195 - 19
16 u = 176
1 u = 176 ÷ 16 = 11
Number of beads in Container B at first
= 7 u + 19
= 7 x 11 + 19
= 77 + 19
= 96
Number of beads in Container C and Container A at first
= 195 - 96
= 99
Container B : Container C and Container A
96 : 99
(÷3)32 : 33
Answer(s): 32 : 33
