Three boxes, B, C and A, contained 450 marbles. Simon 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 removed 89 marbles from 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 A to the total number of marbles in Box B and Box C 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 + 89 |
450 |
| Change |
+ 2x4 =
+ 8 u |
- 1x4 =
- 4 u |
- 89 |
|
| 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 the same. 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 the same. 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 + 89
= 19 u + 89
19 u + 89 = 450
19 u = 450 - 89
19 u = 361
1 u = 361 ÷ 19 = 19
Number of marbles in Box A at first
= 7 u + 89
= 7 x 19 + 89
= 133 + 89
= 222
Number of marbles in Box B and Box C at first
= 450 - 222
= 228
Box A : Box B and Box C
222 : 228
(÷6)37 : 38
Answer(s): 37 : 38
