Three boxes, B, C and A, contained 174 balls. Henry added some balls into Box B and the number of balls in Box B tripled. He took out half of the number of balls from Box C and added another 96 balls into Box A. As a result, the ratio of the number of balls in Box B, Box C and Box A became 12 : 2 : 7. What was the ratio of the number of balls in Box C to the total number of balls in Box B and Box A at first? Give the answer in its lowest term.
| |
Box B |
Box C |
Box A |
Total |
| Before |
1x4 =
4 u |
2x2 =
4 u |
7 u - 96 |
174 |
| Change |
+ 2x4 =
+ 8 u |
- 1x2 =
- 2 u |
+ 96 |
|
| After |
3x4 =
12 u |
1x2 =
2 u |
|
|
Comparing the
3 boxes |
12 u |
2 u |
7 u |
|
The number of balls in Box B in the end is repeated. Make the number of balls in Box B in the end the same. LCM of 3 and 12 is 12.
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 1 and 2 is 2.
Total number of balls at first
= 4 u + 4 u + 7 u - 96
= 15 u - 96
15 u - 96 = 174
15 u = 174 + 96
15 u = 270
1 u = 270 ÷ 15 = 18
Number of balls in Box C at first
= 4 u
= 4 x 18
= 72
Number of balls in Box B and Box A at first
= 174 - 72
= 102
Box C : Box B and Box A
72 : 102
(÷6)12 : 17
Answer(s): 12 : 17
