Three boxes, B, C and A, contained 210 marbles. Ivan added some marbles into Box B and the number of marbles in Box B tripled. He took out half of the number of marbles from Box C and added another 37 marbles into Box A. As a result, the ratio of the number of marbles in Box B, Box C and Box A became 12 : 4 : 7. What was the ratio of the number of marbles in Box C to the total number of marbles 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 |
2x4 = 8 u |
7 u - 37 |
210 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
+ 37 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
12 u |
4 u |
7 u |
|
The number of marbles in Box B in the end is repeated. Make the number of marbles in Box B in the end the same. LCM of 3 and 12 is 12.
The number of marbles in Box C in the end is repeated. Make the number of marbles in Box C in the end the same. LCM of 1 and 4 is 4.
Total number of marbles at first
= 4 u + 8 u + 7 u - 37
= 19 u - 37
19 u - 37 = 210
19 u = 210 + 37
19 u = 247
1 u = 247 ÷ 19 = 13
Number of marbles in Box C at first
= 8 u
= 8 x 13
= 104
Number of marbles in Box B and Box A at first
= 210 - 104
= 106
Box C : Box B and Box A
104 : 106
(÷2)52 : 53
Answer(s): 52 : 53