Three cartons, A, B and C, contained 130 balls. Rael 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 added another 20 balls into Carton C. As a result, the ratio of the number of balls in Carton A, Carton B and Carton C became 12 : 4 : 3. What was the ratio of the number of balls in Carton B to the total number of balls in Carton A and Carton C at first? Give the answer in its lowest term.
| |
Carton A |
Carton B |
Carton C |
Total |
| Before |
1x4 =
4 u |
2x4 =
8 u |
3 u - 20 |
130 |
| Change |
+ 2x4 =
+ 8 u |
- 1x4 =
- 4 u |
+ 20 |
|
| After |
3x4 =
12 u |
1x4 =
4 u |
|
|
Comparing the
3 cartons |
12 u |
4 u |
3 u |
|
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 3 and 12 is 12.
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 1 and 4 is 4.
Total number of balls at first
= 4 u + 8 u + 3 u - 20
= 15 u - 20
15 u - 20 = 130
15 u = 130 + 20
15 u = 150
1 u = 150 ÷ 15 = 10
Number of balls in Carton B at first
= 8 u
= 8 x 10
= 80
Number of balls in Carton A and Carton C at first
= 130 - 80
= 50
Carton B : Carton A and Carton C
80 : 50
(÷10)8 : 5
Answer(s): 8 : 5
