Three cartons, A, B and C, contained 132 marbles. Elijah added some marbles into Carton A and the number of marbles in Carton A tripled. He took out half of the number of marbles from Carton B and added another 66 marbles into Carton C. As a result, the ratio of the number of marbles in Carton A, Carton B and Carton C became 6 : 2 : 5. What was the ratio of the number of marbles in Carton B to the total number of marbles in Carton A and Carton C at first? Give the answer in its lowest term.
|
Carton A |
Carton B |
Carton C |
Total |
Before |
1x2 = 2 u |
2x2 = 4 u |
5 u - 66 |
132 |
Change |
+ 2x2 = + 4 u |
- 1x2 = - 2 u |
+ 66 |
|
After |
3x2 = 6 u |
1x2 = 2 u |
|
|
Comparing the 3 cartons |
6 u |
2 u |
5 u |
|
The number of marbles in Carton A in the end is repeated. Make the number of marbles in Carton A in the end the same. LCM of 3 and 6 is 6.
The number of marbles in Carton B in the end is repeated. Make the number of marbles in Carton B in the end the same. LCM of 1 and 2 is 2.
Total number of marbles at first
= 2 u + 4 u + 5 u - 66
= 11 u - 66
11 u - 66 = 132
11 u = 132 + 66
11 u = 198
1 u = 198 ÷ 11 = 18
Number of marbles in Carton B at first
= 4 u
= 4 x 18
= 72
Number of marbles in Carton A and Carton C at first
= 132 - 72
= 60
Carton B : Carton A and Carton C
72 : 60
(÷12)6 : 5
Answer(s): 6 : 5