Three boxes, A, B and C, contained 363 balls. Glen added some balls into Box A and the number of balls in Box A tripled. He took out half of the number of balls from Box B and removed 75 balls from Box C. As a result, the ratio of the number of balls in Box A, Box B and Box C became 9 : 4 : 5. What was the ratio of the number of balls in Box C to the total number of balls in Box A and Box B at first? Give the answer in its lowest term.
| |
Box A |
Box B |
Box C |
Total |
| Before |
1x3 =
3 u |
2x4 =
8 u |
5 u + 75 |
363 |
| Change |
+ 2x3 =
+ 6 u |
- 1x4 =
- 4 u |
- 75 |
|
| After |
3x3 =
9 u |
1x4 =
4 u |
|
|
Comparing the
3 boxes |
9 u
|
4 u |
5 u |
|
The number of balls in Box A in the end is the same. Make the number of balls in Box A in the end the same. LCM of 3 and 9 is 9.
The number of balls in Box B in the end is the same. Make the number of balls in Box B in the end the same. LCM of 1 and 4 is 4.
Total number of balls at first
= 3 u + 8 u + 5 u + 75
= 16 u + 75
16 u + 75 = 363
16 u = 363 - 75
16 u = 288
1 u = 288 ÷ 16 = 18
Number of balls in Box C at first
= 5 u + 75
= 5 x 18 + 75
= 90 + 75
= 165
Number of balls in Box A and Box B at first
= 363 - 165
= 198
Box C : Box A and Box B
165 : 198
(÷33)5 : 6
Answer(s): 5 : 6
