Three boxes, A, B and C, contained 386 marbles. Fred 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 86 marbles from Box C. As a result, the ratio of the number of marbles in Box A, Box B and Box C became 12 : 4 : 3. 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 |
2x4 =
8 u |
3 u + 86 |
386 |
| Change |
+ 2x4 =
+ 8 u |
- 1x4 =
- 4 u |
- 86 |
|
| After |
3x4 =
12 u |
1x4 =
4 u |
|
|
Comparing the
3 boxes |
12 u
|
4 u |
3 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 4 is 4.
Total number of marbles at first
= 4 u + 8 u + 3 u + 86
= 15 u + 86
15 u + 86 = 386
15 u = 386 - 86
15 u = 300
1 u = 300 ÷ 15 = 20
Number of marbles in Box C at first
= 3 u + 86
= 3 x 20 + 86
= 60 + 86
= 146
Number of marbles in Box A and Box B at first
= 386 - 146
= 240
Box C : Box A and Box B
146 : 240
(÷2)73 : 120
Answer(s): 73 : 120
