Three cartons, C, A and B, contained 310 balls. Nick 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 removed 22 balls from Carton B. As a result, the ratio of the number of balls in Carton C, Carton A and Carton B became 9 : 4 : 5. What was the ratio of the number of balls in Carton B to the total number of balls in Carton C and Carton A at first? Give the answer in its lowest term.
|
Carton C |
Carton A |
Carton B |
Total |
Before |
1x3 = 3 u |
2x4 = 8 u |
5 u + 22 |
310 |
Change |
+ 2x3 = + 6 u |
- 1x4 = - 4 u |
- 22 |
|
After |
3x3 = 9 u |
1x4 = 4 u |
|
|
Comparing the 3 cartons |
9 u
|
4 u |
5 u |
|
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 3 and 9 is 9.
The number of balls in Carton A in the end is the same. 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 + 5 u + 22
= 16 u + 22
16 u + 22 = 310
16 u = 310 - 22
16 u = 288
1 u = 288 ÷ 16 = 18
Number of balls in Carton B at first
= 5 u + 22
= 5 x 18 + 22
= 90 + 22
= 112
Number of balls in Carton C and Carton A at first
= 310 - 112
= 198
Carton B : Carton C and Carton A
112 : 198
(÷2)56 : 99
Answer(s): 56 : 99