Three containers, B, C and A, contained 100 balls. Owen added some balls into Container B and the number of balls in Container B tripled. He took out half of the number of balls from Container C and added another 43 balls into Container A. As a result, the ratio of the number of balls in Container B, Container C and Container A became 6 : 3 : 5. What was the ratio of the number of balls in Container C to the total number of balls in Container B and Container A at first? Give the answer in its lowest term.
| |
Container B |
Container C |
Container A |
Total |
| Before |
1x2 =
2 u |
2x3 =
6 u |
5 u - 43 |
100 |
| Change |
+ 2x2 =
+ 4 u |
- 1x3 =
- 3 u |
+ 43 |
|
| After |
3x2 =
6 u |
1x3 =
3 u |
|
|
Comparing the
3 containers |
6 u |
3 u |
5 u |
|
The number of balls in Container B in the end is repeated. Make the number of balls in Container B in the end the same. LCM of 3 and 6 is 6.
The number of balls in Container C in the end is repeated. Make the number of balls in Container C in the end the same. LCM of 1 and 3 is 3.
Total number of balls at first
= 2 u + 6 u + 5 u - 43
= 13 u - 43
13 u - 43 = 100
13 u = 100 + 43
13 u = 143
1 u = 143 ÷ 13 = 11
Number of balls in Container C at first
= 6 u
= 6 x 11
= 66
Number of balls in Container B and Container A at first
= 100 - 66
= 34
Container C : Container B and Container A
66 : 34
(÷2)33 : 17
Answer(s): 33 : 17
