Three cartons, B, C and A, contained 300 balls. Eric 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 removed 20 balls from Carton A. As a result, the ratio of the number of balls in Carton B, Carton C and Carton A became 9 : 3 : 5. What was the ratio of the number of balls in Carton A to the total number of balls in Carton B and Carton C at first? Give the answer in its lowest term.
| |
Carton B |
Carton C |
Carton A |
Total |
| Before |
1x3 =
3 u |
2x3 =
6 u |
5 u + 20 |
300 |
| Change |
+ 2x3 =
+ 6 u |
- 1x3 =
- 3 u |
- 20 |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
|
|
Comparing the
3 cartons |
9 u
|
3 u |
5 u |
|
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 3 and 9 is 9.
The number of balls in Carton C in the end is the same. 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
= 3 u + 6 u + 5 u + 20
= 14 u + 20
14 u + 20 = 300
14 u = 300 - 20
14 u = 280
1 u = 280 ÷ 14 = 20
Number of balls in Carton A at first
= 5 u + 20
= 5 x 20 + 20
= 100 + 20
= 120
Number of balls in Carton B and Carton C at first
= 300 - 120
= 180
Carton A : Carton B and Carton C
120 : 180
(÷60)2 : 3
Answer(s): 2 : 3
