Three boxes, B, C and A, contained 200 beads. Caden 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 removed 32 beads from Box A. As a result, the ratio of the number of beads in Box B, Box C and Box A became 9 : 3 : 5. What was the ratio of the number of beads in Box A to the total number of beads in Box B and Box C at first? Give the answer in its lowest term.
|
Box B |
Box C |
Box A |
Total |
Before |
1x3 = 3 u |
2x3 = 6 u |
5 u + 32 |
200 |
Change |
+ 2x3 = + 6 u |
- 1x3 = - 3 u |
- 32 |
|
After |
3x3 = 9 u |
1x3 = 3 u |
|
|
Comparing the 3 boxes |
9 u
|
3 u |
5 u |
|
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 3 and 9 is 9.
The number of beads in Box C in the end is the same. Make the number of beads in Box C in the end the same. LCM of 1 and 3 is 3.
Total number of beads at first
= 3 u + 6 u + 5 u + 32
= 14 u + 32
14 u + 32 = 200
14 u = 200 - 32
14 u = 168
1 u = 168 ÷ 14 = 12
Number of beads in Box A at first
= 5 u + 32
= 5 x 12 + 32
= 60 + 32
= 92
Number of beads in Box B and Box C at first
= 200 - 92
= 108
Box A : Box B and Box C
92 : 108
(÷4)23 : 27
Answer(s): 23 : 27