Three boxes, C, A and B, contained 140 beads. Elijah 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 42 beads into Box B. As a result, the ratio of the number of beads in Box C, Box A and Box B became 6 : 3 : 5. 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 |
1x2 = 2 u |
2x3 = 6 u |
5 u - 42 |
140 |
Change |
+ 2x2 = + 4 u |
- 1x3 = - 3 u |
+ 42 |
|
After |
3x2 = 6 u |
1x3 = 3 u |
|
|
Comparing the 3 boxes |
6 u |
3 u |
5 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 6 is 6.
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
= 2 u + 6 u + 5 u - 42
= 13 u - 42
13 u - 42 = 140
13 u = 140 + 42
13 u = 182
1 u = 182 ÷ 13 = 14
Number of beads in Box A at first
= 6 u
= 6 x 14
= 84
Number of beads in Box C and Box B at first
= 140 - 84
= 56
Box A : Box C and Box B
84 : 56
(÷28)3 : 2
Answer(s): 3 : 2