Three boxes, B, C and A, contained 304 marbles. Ethan 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 19 marbles from Box A. As a result, the ratio of the number of marbles in Box B, Box C and Box A became 6 : 2 : 9. 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 |
1x2 = 2 u |
2x2 = 4 u |
9 u + 19 |
304 |
Change |
+ 2x2 = + 4 u |
- 1x2 = - 2 u |
- 19 |
|
After |
3x2 = 6 u |
1x2 = 2 u |
|
|
Comparing the 3 boxes |
6 u
|
2 u |
9 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 6 is 6.
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 2 is 2.
Total number of marbles at first
= 2 u + 4 u + 9 u + 19
= 15 u + 19
15 u + 19 = 304
15 u = 304 - 19
15 u = 285
1 u = 285 ÷ 15 = 19
Number of marbles in Box A at first
= 9 u + 19
= 9 x 19 + 19
= 171 + 19
= 190
Number of marbles in Box B and Box C at first
= 304 - 190
= 114
Box A : Box B and Box C
190 : 114
(÷38)5 : 3
Answer(s): 5 : 3