Three containers, A, B and C, contained 134 balls. Owen added some balls into Container A and the number of balls in Container A tripled. He took out half of the number of balls from Container B and added another 48 balls into Container C. As a result, the ratio of the number of balls in Container A, Container B and Container C became 6 : 3 : 5. What was the ratio of the number of balls in Container B to the total number of balls in Container A and Container C at first? Give the answer in its lowest term.
| |
Container A |
Container B |
Container C |
Total |
| Before |
1x2 =
2 u |
2x3 =
6 u |
5 u - 48 |
134 |
| Change |
+ 2x2 =
+ 4 u |
- 1x3 =
- 3 u |
+ 48 |
|
| After |
3x2 =
6 u |
1x3 =
3 u |
|
|
Comparing the
3 containers |
6 u |
3 u |
5 u |
|
The number of balls in Container A in the end is repeated. Make the number of balls in Container A in the end the same. LCM of 3 and 6 is 6.
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 1 and 3 is 3.
Total number of balls at first
= 2 u + 6 u + 5 u - 48
= 13 u - 48
13 u - 48 = 134
13 u = 134 + 48
13 u = 182
1 u = 182 ÷ 13 = 14
Number of balls in Container B at first
= 6 u
= 6 x 14
= 84
Number of balls in Container A and Container C at first
= 134 - 84
= 50
Container B : Container A and Container C
84 : 50
(÷2)42 : 25
Answer(s): 42 : 25
