Three boxes, B, C and A, contained 198 marbles. Carl 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 16 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 : 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 |
1x2 =
2 u |
2x2 =
4 u |
7 u + 16 |
198 |
| Change |
+ 2x2 =
+ 4 u |
- 1x2 =
- 2 u |
- 16 |
|
| After |
3x2 =
6 u |
1x2 =
2 u |
|
|
Comparing the
3 boxes |
6 u
|
2 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 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 + 7 u + 16
= 13 u + 16
13 u + 16 = 198
13 u = 198 - 16
13 u = 182
1 u = 182 ÷ 13 = 14
Number of marbles in Box A at first
= 7 u + 16
= 7 x 14 + 16
= 98 + 16
= 114
Number of marbles in Box B and Box C at first
= 198 - 114
= 84
Box A : Box B and Box C
114 : 84
(÷6)19 : 14
Answer(s): 19 : 14
