Three boxes, C, A and B, contained 268 balls. Tommy 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 21 balls into Box B. As a result, the ratio of the number of balls in Box C, Box A and Box B became 12 : 2 : 9. 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 |
1x4 =
4 u |
2x2 =
4 u |
9 u - 21 |
268 |
| Change |
+ 2x4 =
+ 8 u |
- 1x2 =
- 2 u |
+ 21 |
|
| After |
3x4 =
12 u |
1x2 =
2 u |
|
|
Comparing the
3 boxes |
12 u |
2 u |
9 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 12 is 12.
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
= 4 u + 4 u + 9 u - 21
= 17 u - 21
17 u - 21 = 268
17 u = 268 + 21
17 u = 289
1 u = 289 ÷ 17 = 17
Number of balls in Box A at first
= 4 u
= 4 x 17
= 68
Number of balls in Box C and Box B at first
= 268 - 68
= 200
Box A : Box C and Box B
68 : 200
(÷4)17 : 50
Answer(s): 17 : 50
