Three boxes, A, B and C, contained 219 marbles. Cole 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 36 marbles into Box C. As a result, the ratio of the number of marbles in Box A, Box B and Box C became 6 : 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 |
1x2 = 2 u |
2x4 = 8 u |
7 u - 36 |
219 |
Change |
+ 2x2 = + 4 u |
- 1x4 = - 4 u |
+ 36 |
|
After |
3x2 = 6 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
6 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 6 is 6.
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
= 2 u + 8 u + 7 u - 36
= 17 u - 36
17 u - 36 = 219
17 u = 219 + 36
17 u = 255
1 u = 255 ÷ 17 = 15
Number of marbles in Box B at first
= 8 u
= 8 x 15
= 120
Number of marbles in Box A and Box C at first
= 219 - 120
= 99
Box B : Box A and Box C
120 : 99
(÷3)40 : 33
Answer(s): 40 : 33