Three containers, C, A and B, contained 219 beads. David 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 21 beads into 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 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 |
1x3 =
3 u |
2x3 =
6 u |
7 u - 21 |
219 |
| Change |
+ 2x3 =
+ 6 u |
- 1x3 =
- 3 u |
+ 21 |
|
| 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 repeated. 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 repeated. 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 - 21
= 16 u - 21
16 u - 21 = 219
16 u = 219 + 21
16 u = 240
1 u = 240 ÷ 16 = 15
Number of beads in Container A at first
= 6 u
= 6 x 15
= 90
Number of beads in Container C and Container B at first
= 219 - 90
= 129
Container A : Container C and Container B
90 : 129
(÷3)30 : 43
Answer(s): 30 : 43
