Three boxes, B, C and A, contained 236 marbles. Oliver 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 44 marbles from Box A. As a result, the ratio of the number of marbles in Box B, Box C and Box A became 9 : 3 : 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 |
1x3 = 3 u |
2x3 = 6 u |
7 u + 44 |
236 |
Change |
+ 2x3 = + 6 u |
- 1x3 = - 3 u |
- 44 |
|
After |
3x3 = 9 u |
1x3 = 3 u |
|
|
Comparing the 3 boxes |
9 u
|
3 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 9 is 9.
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 3 is 3.
Total number of marbles at first
= 3 u + 6 u + 7 u + 44
= 16 u + 44
16 u + 44 = 236
16 u = 236 - 44
16 u = 192
1 u = 192 ÷ 16 = 12
Number of marbles in Box A at first
= 7 u + 44
= 7 x 12 + 44
= 84 + 44
= 128
Number of marbles in Box B and Box C at first
= 236 - 128
= 108
Box A : Box B and Box C
128 : 108
(÷4)32 : 27
Answer(s): 32 : 27