Three boxes, C, A and B, contained 248 balls. John added some balls into Box C and the number of balls in Box C tripled. He took out half of the number of balls from Box A and added another 12 balls into Box B. As a result, the ratio of the number of balls in Box C, Box A and Box B became 6 : 2 : 7. What was the ratio of the number of balls in Box A to the total number of balls 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 |
2x2 =
4 u |
7 u - 12 |
248 |
| Change |
+ 2x2 =
+ 4 u |
- 1x2 =
- 2 u |
+ 12 |
|
| After |
3x2 =
6 u |
1x2 =
2 u |
|
|
Comparing the
3 boxes |
6 u |
2 u |
7 u |
|
The number of balls in Box C in the end is repeated. Make the number of balls in Box C in the end the same. LCM of 3 and 6 is 6.
The number of balls in Box A in the end is repeated. Make the number of balls in Box A in the end the same. LCM of 1 and 2 is 2.
Total number of balls at first
= 2 u + 4 u + 7 u - 12
= 13 u - 12
13 u - 12 = 248
13 u = 248 + 12
13 u = 260
1 u = 260 ÷ 13 = 20
Number of balls in Box A at first
= 4 u
= 4 x 20
= 80
Number of balls in Box C and Box B at first
= 248 - 80
= 168
Box A : Box C and Box B
80 : 168
(÷8)10 : 21
Answer(s): 10 : 21
