Three cartons, A, B and C, contained 370 balls. Jenson 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 30 balls into Carton C. As a result, the ratio of the number of balls in Carton A, Carton B and Carton C became 9 : 4 : 9. 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 |
1x3 = 3 u |
2x4 = 8 u |
9 u - 30 |
370 |
Change |
+ 2x3 = + 6 u |
- 1x4 = - 4 u |
+ 30 |
|
After |
3x3 = 9 u |
1x4 = 4 u |
|
|
Comparing the 3 cartons |
9 u |
4 u |
9 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 9 is 9.
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
= 3 u + 8 u + 9 u - 30
= 20 u - 30
20 u - 30 = 370
20 u = 370 + 30
20 u = 400
1 u = 400 ÷ 20 = 20
Number of balls in Carton B at first
= 8 u
= 8 x 20
= 160
Number of balls in Carton A and Carton C at first
= 370 - 160
= 210
Carton B : Carton A and Carton C
160 : 210
(÷10)16 : 21
Answer(s): 16 : 21