Three boxes, C, A and B, contained 203 marbles. Seth 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 71 marbles from Box B. As a result, the ratio of the number of marbles in Box C, Box A and Box B became 9 : 2 : 5. 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 |
2x2 = 4 u |
5 u + 71 |
203 |
Change |
+ 2x3 = + 6 u |
- 1x2 = - 2 u |
- 71 |
|
After |
3x3 = 9 u |
1x2 = 2 u |
|
|
Comparing the 3 boxes |
9 u
|
2 u |
5 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 2 is 2.
Total number of marbles at first
= 3 u + 4 u + 5 u + 71
= 12 u + 71
12 u + 71 = 203
12 u = 203 - 71
12 u = 132
1 u = 132 ÷ 12 = 11
Number of marbles in Box B at first
= 5 u + 71
= 5 x 11 + 71
= 55 + 71
= 126
Number of marbles in Box C and Box A at first
= 203 - 126
= 77
Box B : Box C and Box A
126 : 77
(÷7)18 : 11
Answer(s): 18 : 11