Three cartons, B, C and A, contained 222 balls. Bobby 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 12 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 : 11. 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 |
11 u - 12 |
222 |
| Change |
+ 2x3 =
+ 6 u |
- 1x2 =
- 2 u |
+ 12 |
|
| After |
3x3 =
9 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
9 u |
2 u |
11 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 + 11 u - 12
= 18 u - 12
18 u - 12 = 222
18 u = 222 + 12
18 u = 234
1 u = 234 ÷ 18 = 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
= 222 - 52
= 170
Carton C : Carton B and Carton A
52 : 170
(÷2)26 : 85
Answer(s): 26 : 85
