Three boxes, B, C and A, contained 530 marbles. Jeremy 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 70 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 : 11. 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 |
11 u + 70 |
530 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
- 70 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
12 u
|
4 u |
11 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 + 11 u + 70
= 23 u + 70
23 u + 70 = 530
23 u = 530 - 70
23 u = 460
1 u = 460 ÷ 23 = 20
Number of marbles in Box A at first
= 11 u + 70
= 11 x 20 + 70
= 220 + 70
= 290
Number of marbles in Box B and Box C at first
= 530 - 290
= 240
Box A : Box B and Box C
290 : 240
(÷10)29 : 24
Answer(s): 29 : 24