Three cartons, B, C and A, contained 212 marbles. Charlie added some marbles into Carton B and the number of marbles in Carton B tripled. He took out half of the number of marbles from Carton C and added another 60 marbles into Carton A. As a result, the ratio of the number of marbles in Carton B, Carton C and Carton A became 9 : 3 : 7. What was the ratio of the number of marbles in Carton C to the total number of marbles in Carton B and Carton A at first? Give the answer in its lowest term.
| |
Carton B |
Carton C |
Carton A |
Total |
| Before |
1x3 =
3 u |
2x3 =
6 u |
7 u - 60 |
212 |
| Change |
+ 2x3 =
+ 6 u |
- 1x3 =
- 3 u |
+ 60 |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
|
|
Comparing the
3 cartons |
9 u |
3 u |
7 u |
|
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 3 and 9 is 9.
The number of marbles in Carton C in the end is repeated. Make the number of marbles in Carton C in the end the same. LCM of 1 and 3 is 3.
Total number of marbles at first
= 3 u + 6 u + 7 u - 60
= 16 u - 60
16 u - 60 = 212
16 u = 212 + 60
16 u = 272
1 u = 272 ÷ 16 = 17
Number of marbles in Carton C at first
= 6 u
= 6 x 17
= 102
Number of marbles in Carton B and Carton A at first
= 212 - 102
= 110
Carton C : Carton B and Carton A
102 : 110
(÷2)51 : 55
Answer(s): 51 : 55
