Three boxes, C, A and B, contained 355 balls. Japheth 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 66 balls from Box B. As a result, the ratio of the number of balls in Box C, Box A and Box B became 6 : 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 |
1x2 = 2 u |
2x4 = 8 u |
7 u + 66 |
355 |
Change |
+ 2x2 = + 4 u |
- 1x4 = - 4 u |
- 66 |
|
After |
3x2 = 6 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
6 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 6 is 6.
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
= 2 u + 8 u + 7 u + 66
= 17 u + 66
17 u + 66 = 355
17 u = 355 - 66
17 u = 289
1 u = 289 ÷ 17 = 17
Number of balls in Box B at first
= 7 u + 66
= 7 x 17 + 66
= 119 + 66
= 185
Number of balls in Box C and Box A at first
= 355 - 185
= 170
Box B : Box C and Box A
185 : 170
(÷5)37 : 34
Answer(s): 37 : 34