Three boxes, A, B and C, contained 292 beads. Zane 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 52 beads from Box C. As a result, the ratio of the number of beads in Box A, Box B and Box C became 6 : 3 : 7. 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 |
1x2 =
2 u |
2x3 =
6 u |
7 u + 52 |
292 |
| Change |
+ 2x2 =
+ 4 u |
- 1x3 =
- 3 u |
- 52 |
|
| After |
3x2 =
6 u |
1x3 =
3 u |
|
|
Comparing the
3 boxes |
6 u
|
3 u |
7 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 6 is 6.
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 3 is 3.
Total number of beads at first
= 2 u + 6 u + 7 u + 52
= 15 u + 52
15 u + 52 = 292
15 u = 292 - 52
15 u = 240
1 u = 240 ÷ 15 = 16
Number of beads in Box C at first
= 7 u + 52
= 7 x 16 + 52
= 112 + 52
= 164
Number of beads in Box A and Box B at first
= 292 - 164
= 128
Box C : Box A and Box B
164 : 128
(÷4)41 : 32
Answer(s): 41 : 32
