Three boxes, B, C and A, contained 270 balls. Rael 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 added another 15 balls into Box A. As a result, the ratio of the number of balls in Box B, Box C and Box A became 12 : 3 : 5. What was the ratio of the number of balls in Box C to the total number of balls in Box B and Box A at first? Give the answer in its lowest term.
| |
Box B |
Box C |
Box A |
Total |
| Before |
1x4 =
4 u |
2x3 =
6 u |
5 u - 15 |
270 |
| Change |
+ 2x4 =
+ 8 u |
- 1x3 =
- 3 u |
+ 15 |
|
| After |
3x4 =
12 u |
1x3 =
3 u |
|
|
Comparing the
3 boxes |
12 u |
3 u |
5 u |
|
The number of balls in Box B in the end is repeated. Make the number of balls in Box B in the end the same. LCM of 3 and 12 is 12.
The number of balls in Box C in the end is repeated. Make the number of balls in Box C in the end the same. LCM of 1 and 3 is 3.
Total number of balls at first
= 4 u + 6 u + 5 u - 15
= 15 u - 15
15 u - 15 = 270
15 u = 270 + 15
15 u = 285
1 u = 285 ÷ 15 = 19
Number of balls in Box C at first
= 6 u
= 6 x 19
= 114
Number of balls in Box B and Box A at first
= 270 - 114
= 156
Box C : Box B and Box A
114 : 156
(÷6)19 : 26
Answer(s): 19 : 26
