Three boxes, C, A and B, contained 164 beads. Will 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 16 beads into Box B. As a result, the ratio of the number of beads in Box C, Box A and Box B became 12 : 4 : 3. 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 |
1x4 = 4 u |
2x4 = 8 u |
3 u - 16 |
164 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
+ 16 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 boxes |
12 u |
4 u |
3 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 12 is 12.
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
= 4 u + 8 u + 3 u - 16
= 15 u - 16
15 u - 16 = 164
15 u = 164 + 16
15 u = 180
1 u = 180 ÷ 15 = 12
Number of beads in Box A at first
= 8 u
= 8 x 12
= 96
Number of beads in Box C and Box B at first
= 164 - 96
= 68
Box A : Box C and Box B
96 : 68
(÷4)24 : 17
Answer(s): 24 : 17