Three boxes, C, A and B, contained 194 beads. Liam added some beads into Box C and the number of beads in Box C tripled. He took out half of the number of beads from Box A and added another 46 beads into Box B. As a result, the ratio of the number of beads in Box C, Box A and Box B became 6 : 4 : 5. What was the ratio of the number of beads in Box A to the total number of beads in Box C and Box B at first? Give the answer in its lowest term.
|
Box C |
Box A |
Box B |
Total |
Before |
1x2 = 2 u |
2x4 = 8 u |
5 u - 46 |
194 |
Change |
+ 2x2 = + 4 u |
- 1x4 = - 4 u |
+ 46 |
|
After |
3x2 = 6 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
6 u |
4 u |
5 u |
|
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 3 and 6 is 6.
The number of beads in Box A in the end is repeated. Make the number of beads in Box A in the end the same. LCM of 1 and 4 is 4.
Total number of beads at first
= 2 u + 8 u + 5 u - 46
= 15 u - 46
15 u - 46 = 194
15 u = 194 + 46
15 u = 240
1 u = 240 ÷ 15 = 16
Number of beads in Box A at first
= 8 u
= 8 x 16
= 128
Number of beads in Box C and Box B at first
= 194 - 128
= 66
Box A : Box C and Box B
128 : 66
(÷2)64 : 33
Answer(s): 64 : 33