Three cartons, B, C and A, contained 182 balls. Dylan 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 56 balls into Carton A. As a result, the ratio of the number of balls in Carton B, Carton C and Carton A became 12 : 3 : 7. 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 |
2x3 = 6 u |
7 u - 56 |
182 |
Change |
+ 2x4 = + 8 u |
- 1x3 = - 3 u |
+ 56 |
|
After |
3x4 = 12 u |
1x3 = 3 u |
|
|
Comparing the 3 cartons |
12 u |
3 u |
7 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 3 is 3.
Total number of balls at first
= 4 u + 6 u + 7 u - 56
= 17 u - 56
17 u - 56 = 182
17 u = 182 + 56
17 u = 238
1 u = 238 ÷ 17 = 14
Number of balls in Carton C at first
= 6 u
= 6 x 14
= 84
Number of balls in Carton B and Carton A at first
= 182 - 84
= 98
Carton C : Carton B and Carton A
84 : 98
(÷14)6 : 7
Answer(s): 6 : 7