Three boxes, A, B and C, contained 328 beads. Billy 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 added another 33 beads into Box C. As a result, the ratio of the number of beads in Box A, Box B and Box C became 12 : 4 : 7. What was the ratio of the number of beads in Box B to the total number of beads in Box A and Box C at first? Give the answer in its lowest term.
| |
Box A |
Box B |
Box C |
Total |
| Before |
1x4 =
4 u |
2x4 =
8 u |
7 u - 33 |
328 |
| Change |
+ 2x4 =
+ 8 u |
- 1x4 =
- 4 u |
+ 33 |
|
| After |
3x4 =
12 u |
1x4 =
4 u |
|
|
Comparing the
3 boxes |
12 u |
4 u |
7 u |
|
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 3 and 12 is 12.
The number of beads in Box B in the end is repeated. Make the number of beads in Box B in the end the same. LCM of 1 and 4 is 4.
Total number of beads at first
= 4 u + 8 u + 7 u - 33
= 19 u - 33
19 u - 33 = 328
19 u = 328 + 33
19 u = 361
1 u = 361 ÷ 19 = 19
Number of beads in Box B at first
= 8 u
= 8 x 19
= 152
Number of beads in Box A and Box C at first
= 328 - 152
= 176
Box B : Box A and Box C
152 : 176
(÷8)19 : 22
Answer(s): 19 : 22
