Three cartons, C, A and B, contained 240 balls. Dylan added some balls into Carton C and the number of balls in Carton C tripled. He took out half of the number of balls from Carton A and added another 48 balls into Carton B. As a result, the ratio of the number of balls in Carton C, Carton A and Carton B became 9 : 4 : 7. What was the ratio of the number of balls in Carton A to the total number of balls in Carton C and Carton B at first? Give the answer in its lowest term.
| |
Carton C |
Carton A |
Carton B |
Total |
| Before |
1x3 =
3 u |
2x4 =
8 u |
7 u - 48 |
240 |
| Change |
+ 2x3 =
+ 6 u |
- 1x4 =
- 4 u |
+ 48 |
|
| After |
3x3 =
9 u |
1x4 =
4 u |
|
|
Comparing the
3 cartons |
9 u |
4 u |
7 u |
|
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 3 and 9 is 9.
The number of balls in Carton A in the end is repeated. Make the number of balls in Carton A in the end the same. LCM of 1 and 4 is 4.
Total number of balls at first
= 3 u + 8 u + 7 u - 48
= 18 u - 48
18 u - 48 = 240
18 u = 240 + 48
18 u = 288
1 u = 288 ÷ 18 = 16
Number of balls in Carton A at first
= 8 u
= 8 x 16
= 128
Number of balls in Carton C and Carton B at first
= 240 - 128
= 112
Carton A : Carton C and Carton B
128 : 112
(÷16)8 : 7
Answer(s): 8 : 7
