Three boxes, A, B and C, contained 168 beads. Neave 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 92 beads into Box C. As a result, the ratio of the number of beads in Box A, Box B and Box C became 6 : 2 : 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 |
1x2 =
2 u |
2x2 =
4 u |
7 u - 92 |
168 |
| Change |
+ 2x2 =
+ 4 u |
- 1x2 =
- 2 u |
+ 92 |
|
| After |
3x2 =
6 u |
1x2 =
2 u |
|
|
Comparing the
3 boxes |
6 u |
2 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 6 is 6.
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 2 is 2.
Total number of beads at first
= 2 u + 4 u + 7 u - 92
= 13 u - 92
13 u - 92 = 168
13 u = 168 + 92
13 u = 260
1 u = 260 ÷ 13 = 20
Number of beads in Box B at first
= 4 u
= 4 x 20
= 80
Number of beads in Box A and Box C at first
= 168 - 80
= 88
Box B : Box A and Box C
80 : 88
(÷8)10 : 11
Answer(s): 10 : 11
