Three boxes, C, A and B, contained 225 balls. Wesley added some balls into Box C and the number of balls in Box C tripled. He took out half of the number of balls from Box A and removed 45 balls from Box B. As a result, the ratio of the number of balls in Box C, Box A and Box B became 9 : 4 : 7. What was the ratio of the number of balls in Box B to the total number of balls in Box C and Box A at first? Give the answer in its lowest term.
| |
Box C |
Box A |
Box B |
Total |
| Before |
1x3 =
3 u |
2x4 =
8 u |
7 u + 45 |
225 |
| Change |
+ 2x3 =
+ 6 u |
- 1x4 =
- 4 u |
- 45 |
|
| After |
3x3 =
9 u |
1x4 =
4 u |
|
|
Comparing the
3 boxes |
9 u
|
4 u |
7 u |
|
The number of balls in Box C in the end is the same. Make the number of balls in Box C in the end the same. LCM of 3 and 9 is 9.
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 1 and 4 is 4.
Total number of balls at first
= 3 u + 8 u + 7 u + 45
= 18 u + 45
18 u + 45 = 225
18 u = 225 - 45
18 u = 180
1 u = 180 ÷ 18 = 10
Number of balls in Box B at first
= 7 u + 45
= 7 x 10 + 45
= 70 + 45
= 115
Number of balls in Box C and Box A at first
= 225 - 115
= 110
Box B : Box C and Box A
115 : 110
(÷5)23 : 22
Answer(s): 23 : 22
