Three boxes, B, C and A, contained 146 beads. Fabian added some beads into Box B and the number of beads in Box B tripled. He took out half of the number of beads from Box C and added another 58 beads into Box A. As a result, the ratio of the number of beads in Box B, Box C and Box A became 12 : 4 : 5. What was the ratio of the number of beads in Box C to the total number of beads in Box B and Box A at first? Give the answer in its lowest term.
|
Box B |
Box C |
Box A |
Total |
Before |
1x4 = 4 u |
2x4 = 8 u |
5 u - 58 |
146 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
+ 58 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
12 u |
4 u |
5 u |
|
The number of beads in Box B in the end is repeated. Make the number of beads in Box B in the end the same. LCM of 3 and 12 is 12.
The number of beads in Box C in the end is repeated. Make the number of beads in Box C in the end the same. LCM of 1 and 4 is 4.
Total number of beads at first
= 4 u + 8 u + 5 u - 58
= 17 u - 58
17 u - 58 = 146
17 u = 146 + 58
17 u = 204
1 u = 204 ÷ 17 = 12
Number of beads in Box C at first
= 8 u
= 8 x 12
= 96
Number of beads in Box B and Box A at first
= 146 - 96
= 50
Box C : Box B and Box A
96 : 50
(÷2)48 : 25
Answer(s): 48 : 25