Three boxes, C, A and B, contained 246 marbles. Ahmad added some marbles into Box C and the number of marbles in Box C tripled. He took out half of the number of marbles from Box A and removed 46 marbles from Box B. As a result, the ratio of the number of marbles in Box C, Box A and Box B became 9 : 4 : 9. What was the ratio of the number of marbles in Box B to the total number of marbles 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 |
9 u + 46 |
246 |
Change |
+ 2x3 = + 6 u |
- 1x4 = - 4 u |
- 46 |
|
After |
3x3 = 9 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
9 u
|
4 u |
9 u |
|
The number of marbles in Box C in the end is the same. Make the number of marbles in Box C in the end the same. LCM of 3 and 9 is 9.
The number of marbles in Box A in the end is the same. Make the number of marbles in Box A in the end the same. LCM of 1 and 4 is 4.
Total number of marbles at first
= 3 u + 8 u + 9 u + 46
= 20 u + 46
20 u + 46 = 246
20 u = 246 - 46
20 u = 200
1 u = 200 ÷ 20 = 10
Number of marbles in Box B at first
= 9 u + 46
= 9 x 10 + 46
= 90 + 46
= 136
Number of marbles in Box C and Box A at first
= 246 - 136
= 110
Box B : Box C and Box A
136 : 110
(÷2)68 : 55
Answer(s): 68 : 55