Three boxes, B, C and A, contained 316 marbles. Vaidev 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 50 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 + 50 |
316 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
- 50 |
|
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 + 50
= 19 u + 50
19 u + 50 = 316
19 u = 316 - 50
19 u = 266
1 u = 266 ÷ 19 = 14
Number of marbles in Box A at first
= 7 u + 50
= 7 x 14 + 50
= 98 + 50
= 148
Number of marbles in Box B and Box C at first
= 316 - 148
= 168
Box A : Box B and Box C
148 : 168
(÷4)37 : 42
Answer(s): 37 : 42