Three boxes, C, A and B, contained 96 beads. Cole 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 34 beads into Box B. As a result, the ratio of the number of beads in Box C, Box A and Box B became 6 : 3 : 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 |
2x3 =
6 u |
5 u - 34 |
96 |
| Change |
+ 2x2 =
+ 4 u |
- 1x3 =
- 3 u |
+ 34 |
|
| After |
3x2 =
6 u |
1x3 =
3 u |
|
|
Comparing the
3 boxes |
6 u |
3 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 3 is 3.
Total number of beads at first
= 2 u + 6 u + 5 u - 34
= 13 u - 34
13 u - 34 = 96
13 u = 96 + 34
13 u = 130
1 u = 130 ÷ 13 = 10
Number of beads in Box A at first
= 6 u
= 6 x 10
= 60
Number of beads in Box C and Box B at first
= 96 - 60
= 36
Box A : Box C and Box B
60 : 36
(÷12)5 : 3
Answer(s): 5 : 3
