Three boxes, C, A and B, contained 312 beads. Howard 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 68 beads into Box B. As a result, the ratio of the number of beads in Box C, Box A and Box B became 9 : 3 : 11. 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 |
1x3 = 3 u |
2x3 = 6 u |
11 u - 68 |
312 |
Change |
+ 2x3 = + 6 u |
- 1x3 = - 3 u |
+ 68 |
|
After |
3x3 = 9 u |
1x3 = 3 u |
|
|
Comparing the 3 boxes |
9 u |
3 u |
11 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 9 is 9.
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 3 is 3.
Total number of beads at first
= 3 u + 6 u + 11 u - 68
= 20 u - 68
20 u - 68 = 312
20 u = 312 + 68
20 u = 380
1 u = 380 ÷ 20 = 19
Number of beads in Box A at first
= 6 u
= 6 x 19
= 114
Number of beads in Box C and Box B at first
= 312 - 114
= 198
Box A : Box C and Box B
114 : 198
(÷6)19 : 33
Answer(s): 19 : 33