Three containers, A, B and C, contained 332 balls. Cody 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 removed 52 balls from Container C. As a result, the ratio of the number of balls in Container A, Container B and Container C became 9 : 4 : 9. What was the ratio of the number of balls in Container C to the total number of balls in Container A and Container B at first? Give the answer in its lowest term.
| |
Container A |
Container B |
Container C |
Total |
| Before |
1x3 =
3 u |
2x4 =
8 u |
9 u + 52 |
332 |
| Change |
+ 2x3 =
+ 6 u |
- 1x4 =
- 4 u |
- 52 |
|
| After |
3x3 =
9 u |
1x4 =
4 u |
|
|
Comparing the
3 containers |
9 u
|
4 u |
9 u |
|
The number of balls in Container A in the end is the same. Make the number of balls in Container A in the end the same. LCM of 3 and 9 is 9.
The number of balls in Container B in the end is the same. Make the number of balls in Container B in the end the same. LCM of 1 and 4 is 4.
Total number of balls at first
= 3 u + 8 u + 9 u + 52
= 20 u + 52
20 u + 52 = 332
20 u = 332 - 52
20 u = 280
1 u = 280 ÷ 20 = 14
Number of balls in Container C at first
= 9 u + 52
= 9 x 14 + 52
= 126 + 52
= 178
Number of balls in Container A and Container B at first
= 332 - 178
= 154
Container C : Container A and Container B
178 : 154
(÷2)89 : 77
Answer(s): 89 : 77
