Three cartons, A, B and C, contained 258 marbles. Andy 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 removed 78 marbles from Carton C. As a result, the ratio of the number of marbles in Carton A, Carton B and Carton C became 6 : 2 : 9. What was the ratio of the number of marbles in Carton C to the total number of marbles in Carton A and Carton B at first? Give the answer in its lowest term.
|
Carton A |
Carton B |
Carton C |
Total |
Before |
1x2 = 2 u |
2x2 = 4 u |
9 u + 78 |
258 |
Change |
+ 2x2 = + 4 u |
- 1x2 = - 2 u |
- 78 |
|
After |
3x2 = 6 u |
1x2 = 2 u |
|
|
Comparing the 3 cartons |
6 u
|
2 u |
9 u |
|
The number of marbles in Carton A in the end is the same. 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 the same. 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 + 9 u + 78
= 15 u + 78
15 u + 78 = 258
15 u = 258 - 78
15 u = 180
1 u = 180 ÷ 15 = 12
Number of marbles in Carton C at first
= 9 u + 78
= 9 x 12 + 78
= 108 + 78
= 186
Number of marbles in Carton A and Carton B at first
= 258 - 186
= 72
Carton C : Carton A and Carton B
186 : 72
(÷6)31 : 12
Answer(s): 31 : 12