Three cartons, B, C and A, contained 120 balls. Bryan 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 62 balls into Carton A. As a result, the ratio of the number of balls in Carton B, Carton C and Carton A became 9 : 2 : 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 |
1x3 = 3 u |
2x2 = 4 u |
7 u - 62 |
120 |
Change |
+ 2x3 = + 6 u |
- 1x2 = - 2 u |
+ 62 |
|
After |
3x3 = 9 u |
1x2 = 2 u |
|
|
Comparing the 3 cartons |
9 u |
2 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 9 is 9.
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 2 is 2.
Total number of balls at first
= 3 u + 4 u + 7 u - 62
= 14 u - 62
14 u - 62 = 120
14 u = 120 + 62
14 u = 182
1 u = 182 ÷ 14 = 13
Number of balls in Carton C at first
= 4 u
= 4 x 13
= 52
Number of balls in Carton B and Carton A at first
= 120 - 52
= 68
Carton C : Carton B and Carton A
52 : 68
(÷4)13 : 17
Answer(s): 13 : 17