Three boxes, B, C and A, contained 273 balls. Ivan added some balls into Box B and the number of balls in Box B tripled. He took out half of the number of balls from Box C and removed 93 balls from Box A. As a result, the ratio of the number of balls in Box B, Box C and Box A became 9 : 4 : 1. What was the ratio of the number of balls in Box A to the total number of balls in Box B and Box C at first? Give the answer in its lowest term.
| |
Box B |
Box C |
Box A |
Total |
| Before |
1x3 =
3 u |
2x4 =
8 u |
1 u + 93 |
273 |
| Change |
+ 2x3 =
+ 6 u |
- 1x4 =
- 4 u |
- 93 |
|
| After |
3x3 =
9 u |
1x4 =
4 u |
|
|
Comparing the
3 boxes |
9 u
|
4 u |
1 u |
|
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 3 and 9 is 9.
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 1 and 4 is 4.
Total number of balls at first
= 3 u + 8 u + 1 u + 93
= 12 u + 93
12 u + 93 = 273
12 u = 273 - 93
12 u = 180
1 u = 180 ÷ 12 = 15
Number of balls in Box A at first
= 1 u + 93
= 1 x 15 + 93
= 15 + 93
= 108
Number of balls in Box B and Box C at first
= 273 - 108
= 165
Box A : Box B and Box C
108 : 165
(÷3)36 : 55
Answer(s): 36 : 55
