Three boxes, A, B and C, contained 172 marbles. Tom added some marbles into Box A and the number of marbles in Box A tripled. He took out half of the number of marbles from Box B and added another 62 marbles into Box C. As a result, the ratio of the number of marbles in Box A, Box B and Box C became 9 : 4 : 7. What was the ratio of the number of marbles in Box B to the total number of marbles in Box A and Box C at first? Give the answer in its lowest term.
|
Box A |
Box B |
Box C |
Total |
Before |
1x3 = 3 u |
2x4 = 8 u |
7 u - 62 |
172 |
Change |
+ 2x3 = + 6 u |
- 1x4 = - 4 u |
+ 62 |
|
After |
3x3 = 9 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
9 u |
4 u |
7 u |
|
The number of marbles in Box A in the end is repeated. Make the number of marbles in Box A in the end the same. LCM of 3 and 9 is 9.
The number of marbles in Box B in the end is repeated. Make the number of marbles in Box B in the end the same. LCM of 1 and 4 is 4.
Total number of marbles at first
= 3 u + 8 u + 7 u - 62
= 18 u - 62
18 u - 62 = 172
18 u = 172 + 62
18 u = 234
1 u = 234 ÷ 18 = 13
Number of marbles in Box B at first
= 8 u
= 8 x 13
= 104
Number of marbles in Box A and Box C at first
= 172 - 104
= 68
Box B : Box A and Box C
104 : 68
(÷4)26 : 17
Answer(s): 26 : 17