Three boxes, C, A and B, contained 230 balls. George 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 added another 59 balls into Box B. As a result, the ratio of the number of balls in Box C, Box A and Box B became 12 : 4 : 5. What was the ratio of the number of balls in Box A to the total number of balls in Box C and Box B at first? Give the answer in its lowest term.
|
Box C |
Box A |
Box B |
Total |
Before |
1x4 = 4 u |
2x4 = 8 u |
5 u - 59 |
230 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
+ 59 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
12 u |
4 u |
5 u |
|
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 3 and 12 is 12.
The number of balls in Box A in the end is repeated. 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
= 4 u + 8 u + 5 u - 59
= 17 u - 59
17 u - 59 = 230
17 u = 230 + 59
17 u = 289
1 u = 289 ÷ 17 = 17
Number of balls in Box A at first
= 8 u
= 8 x 17
= 136
Number of balls in Box C and Box B at first
= 230 - 136
= 94
Box A : Box C and Box B
136 : 94
(÷2)68 : 47
Answer(s): 68 : 47