Three boxes, B, C and A, contained 128 marbles. Glen 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 added another 48 marbles into Box A. As a result, the ratio of the number of marbles in Box B, Box C and Box A became 9 : 4 : 5. What was the ratio of the number of marbles in Box C to the total number of marbles in Box B and Box A at first? Give the answer in its lowest term.
|
Box B |
Box C |
Box A |
Total |
Before |
1x3 = 3 u |
2x4 = 8 u |
5 u - 48 |
128 |
Change |
+ 2x3 = + 6 u |
- 1x4 = - 4 u |
+ 48 |
|
After |
3x3 = 9 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
9 u |
4 u |
5 u |
|
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 3 and 9 is 9.
The number of marbles in Box C in the end is repeated. 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
= 3 u + 8 u + 5 u - 48
= 16 u - 48
16 u - 48 = 128
16 u = 128 + 48
16 u = 176
1 u = 176 ÷ 16 = 11
Number of marbles in Box C at first
= 8 u
= 8 x 11
= 88
Number of marbles in Box B and Box A at first
= 128 - 88
= 40
Box C : Box B and Box A
88 : 40
(÷8)11 : 5
Answer(s): 11 : 5