Three boxes, A, B and C, contained 134 beads. Justin added some beads into Box A and the number of beads in Box A tripled. He took out half of the number of beads from Box B and removed 13 beads from Box C. As a result, the ratio of the number of beads in Box A, Box B and Box C became 12 : 2 : 3. What was the ratio of the number of beads in Box C to the total number of beads in Box A and Box B at first? Give the answer in its lowest term.
|
Box A |
Box B |
Box C |
Total |
Before |
1x4 = 4 u |
2x2 = 4 u |
3 u + 13 |
134 |
Change |
+ 2x4 = + 8 u |
- 1x2 = - 2 u |
- 13 |
|
After |
3x4 = 12 u |
1x2 = 2 u |
|
|
Comparing the 3 boxes |
12 u
|
2 u |
3 u |
|
The number of beads in Box A in the end is the same. Make the number of beads in Box A in the end the same. LCM of 3 and 12 is 12.
The number of beads in Box B in the end is the same. Make the number of beads in Box B in the end the same. LCM of 1 and 2 is 2.
Total number of beads at first
= 4 u + 4 u + 3 u + 13
= 11 u + 13
11 u + 13 = 134
11 u = 134 - 13
11 u = 121
1 u = 121 ÷ 11 = 11
Number of beads in Box C at first
= 3 u + 13
= 3 x 11 + 13
= 33 + 13
= 46
Number of beads in Box A and Box B at first
= 134 - 46
= 88
Box C : Box A and Box B
46 : 88
(÷2)23 : 44
Answer(s): 23 : 44