Three cartons, B, C and A, contained 328 balls. Carl added some balls into Carton B and the number of balls in Carton B tripled. He took out half of the number of balls from Carton C and added another 29 balls into Carton A. As a result, the ratio of the number of balls in Carton B, Carton C and Carton A became 12 : 4 : 9. What was the ratio of the number of balls in Carton C to the total number of balls in Carton B and Carton A at first? Give the answer in its lowest term.
|
Carton B |
Carton C |
Carton A |
Total |
Before |
1x4 = 4 u |
2x4 = 8 u |
9 u - 29 |
328 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
+ 29 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 cartons |
12 u |
4 u |
9 u |
|
The number of balls in Carton B in the end is repeated. Make the number of balls in Carton B in the end the same. LCM of 3 and 12 is 12.
The number of balls in Carton C in the end is repeated. Make the number of balls in Carton C in the end the same. LCM of 1 and 4 is 4.
Total number of balls at first
= 4 u + 8 u + 9 u - 29
= 21 u - 29
21 u - 29 = 328
21 u = 328 + 29
21 u = 357
1 u = 357 ÷ 21 = 17
Number of balls in Carton C at first
= 8 u
= 8 x 17
= 136
Number of balls in Carton B and Carton A at first
= 328 - 136
= 192
Carton C : Carton B and Carton A
136 : 192
(÷8)17 : 24
Answer(s): 17 : 24