Three cartons, A, B and C, contained 154 balls. Bobby added some balls into Carton A and the number of balls in Carton A tripled. He took out half of the number of balls from Carton B and removed 28 balls from Carton C. As a result, the ratio of the number of balls in Carton A, Carton B and Carton C became 6 : 2 : 3. What was the ratio of the number of balls in Carton C to the total number of balls in Carton A and Carton B at first? Give the answer in its lowest term.
| |
Carton A |
Carton B |
Carton C |
Total |
| Before |
1x2 =
2 u |
2x2 =
4 u |
3 u + 28 |
154 |
| Change |
+ 2x2 =
+ 4 u |
- 1x2 =
- 2 u |
- 28 |
|
| After |
3x2 =
6 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
6 u
|
2 u |
3 u |
|
The number of balls in Carton A in the end is the same. Make the number of balls in Carton A in the end the same. LCM of 3 and 6 is 6.
The number of balls in Carton B in the end is the same. Make the number of balls in Carton B in the end the same. LCM of 1 and 2 is 2.
Total number of balls at first
= 2 u + 4 u + 3 u + 28
= 9 u + 28
9 u + 28 = 154
9 u = 154 - 28
9 u = 126
1 u = 126 ÷ 9 = 14
Number of balls in Carton C at first
= 3 u + 28
= 3 x 14 + 28
= 42 + 28
= 70
Number of balls in Carton A and Carton B at first
= 154 - 70
= 84
Carton C : Carton A and Carton B
70 : 84
(÷14)5 : 6
Answer(s): 5 : 6
