Three cartons, C, A and B, contained 180 balls. Jenson 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 15 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 : 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 |
1x2 = 2 u |
2x2 = 4 u |
5 u + 15 |
180 |
Change |
+ 2x2 = + 4 u |
- 1x2 = - 2 u |
- 15 |
|
After |
3x2 = 6 u |
1x2 = 2 u |
|
|
Comparing the 3 cartons |
6 u
|
2 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 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 + 5 u + 15
= 11 u + 15
11 u + 15 = 180
11 u = 180 - 15
11 u = 165
1 u = 165 ÷ 11 = 15
Number of balls in Carton B at first
= 5 u + 15
= 5 x 15 + 15
= 75 + 15
= 90
Number of balls in Carton C and Carton A at first
= 180 - 90
= 90
Carton B : Carton C and Carton A
90 : 90
(÷90)1 : 1
Answer(s): 1 : 1