Three boxes, B, C and A, contained 303 beads. Julian 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 added another 37 beads into Box A. As a result, the ratio of the number of beads in Box B, Box C and Box A became 9 : 3 : 11. What was the ratio of the number of beads in Box C to the total number of beads in Box B and Box A at first? Give the answer in its lowest term.
|
Box B |
Box C |
Box A |
Total |
Before |
1x3 = 3 u |
2x3 = 6 u |
11 u - 37 |
303 |
Change |
+ 2x3 = + 6 u |
- 1x3 = - 3 u |
+ 37 |
|
After |
3x3 = 9 u |
1x3 = 3 u |
|
|
Comparing the 3 boxes |
9 u |
3 u |
11 u |
|
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 3 and 9 is 9.
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 1 and 3 is 3.
Total number of beads at first
= 3 u + 6 u + 11 u - 37
= 20 u - 37
20 u - 37 = 303
20 u = 303 + 37
20 u = 340
1 u = 340 ÷ 20 = 17
Number of beads in Box C at first
= 6 u
= 6 x 17
= 102
Number of beads in Box B and Box A at first
= 303 - 102
= 201
Box C : Box B and Box A
102 : 201
(÷3)34 : 67
Answer(s): 34 : 67