Three cartons, C, A and B, contained 322 balls. Wesley 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 84 balls from Carton B. As a result, the ratio of the number of balls in Carton C, Carton A and Carton B became 6 : 2 : 11. 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 |
1x2 =
2 u |
2x2 =
4 u |
11 u + 84 |
322 |
| Change |
+ 2x2 =
+ 4 u |
- 1x2 =
- 2 u |
- 84 |
|
| After |
3x2 =
6 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
6 u
|
2 u |
11 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 6 is 6.
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 2 is 2.
Total number of balls at first
= 2 u + 4 u + 11 u + 84
= 17 u + 84
17 u + 84 = 322
17 u = 322 - 84
17 u = 238
1 u = 238 ÷ 17 = 14
Number of balls in Carton B at first
= 11 u + 84
= 11 x 14 + 84
= 154 + 84
= 238
Number of balls in Carton C and Carton A at first
= 322 - 238
= 84
Carton B : Carton C and Carton A
238 : 84
(÷14)17 : 6
Answer(s): 17 : 6
