Three containers, B, C and A, contained 400 marbles. Billy added some marbles into Container B and the number of marbles in Container B tripled. He took out half of the number of marbles from Container C and removed 20 marbles from Container A. As a result, the ratio of the number of marbles in Container B, Container C and Container A became 12 : 4 : 7. What was the ratio of the number of marbles in Container A to the total number of marbles in Container B and Container C at first? Give the answer in its lowest term.
| |
Container B |
Container C |
Container A |
Total |
| Before |
1x4 =
4 u |
2x4 =
8 u |
7 u + 20 |
400 |
| Change |
+ 2x4 =
+ 8 u |
- 1x4 =
- 4 u |
- 20 |
|
| After |
3x4 =
12 u |
1x4 =
4 u |
|
|
Comparing the
3 containers |
12 u
|
4 u |
7 u |
|
The number of marbles in Container B in the end is the same. Make the number of marbles in Container B in the end the same. LCM of 3 and 12 is 12.
The number of marbles in Container C in the end is the same. Make the number of marbles in Container 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 + 20
= 19 u + 20
19 u + 20 = 400
19 u = 400 - 20
19 u = 380
1 u = 380 ÷ 19 = 20
Number of marbles in Container A at first
= 7 u + 20
= 7 x 20 + 20
= 140 + 20
= 160
Number of marbles in Container B and Container C at first
= 400 - 160
= 240
Container A : Container B and Container C
160 : 240
(÷80)2 : 3
Answer(s): 2 : 3
