Three boxes, A, B and C, contained 418 marbles. Jack added some marbles into Box A and the number of marbles in Box A tripled. He took out half of the number of marbles from Box B and removed 40 marbles from Box C. As a result, the ratio of the number of marbles in Box A, Box B and Box C became 12 : 3 : 11. What was the ratio of the number of marbles in Box C to the total number of marbles in Box A and Box B at first? Give the answer in its lowest term.
|
Box A |
Box B |
Box C |
Total |
Before |
1x4 = 4 u |
2x3 = 6 u |
11 u + 40 |
418 |
Change |
+ 2x4 = + 8 u |
- 1x3 = - 3 u |
- 40 |
|
After |
3x4 = 12 u |
1x3 = 3 u |
|
|
Comparing the 3 boxes |
12 u
|
3 u |
11 u |
|
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 3 and 12 is 12.
The number of marbles in Box B in the end is the same. Make the number of marbles in Box B in the end the same. LCM of 1 and 3 is 3.
Total number of marbles at first
= 4 u + 6 u + 11 u + 40
= 21 u + 40
21 u + 40 = 418
21 u = 418 - 40
21 u = 378
1 u = 378 ÷ 21 = 18
Number of marbles in Box C at first
= 11 u + 40
= 11 x 18 + 40
= 198 + 40
= 238
Number of marbles in Box A and Box B at first
= 418 - 238
= 180
Box C : Box A and Box B
238 : 180
(÷2)119 : 90
Answer(s): 119 : 90