Three cartons, B, C and A, contained 270 balls. Liam 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 70 balls into Carton A. As a result, the ratio of the number of balls in Carton B, Carton C and Carton A became 12 : 2 : 9. 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 |
2x2 =
4 u |
9 u - 70 |
270 |
| Change |
+ 2x4 =
+ 8 u |
- 1x2 =
- 2 u |
+ 70 |
|
| After |
3x4 =
12 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
12 u |
2 u |
9 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 2 is 2.
Total number of balls at first
= 4 u + 4 u + 9 u - 70
= 17 u - 70
17 u - 70 = 270
17 u = 270 + 70
17 u = 340
1 u = 340 ÷ 17 = 20
Number of balls in Carton C at first
= 4 u
= 4 x 20
= 80
Number of balls in Carton B and Carton A at first
= 270 - 80
= 190
Carton C : Carton B and Carton A
80 : 190
(÷10)8 : 19
Answer(s): 8 : 19
