Three cartons, A, B and C, contained 202 marbles. Howard 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 49 marbles from Carton C. As a result, the ratio of the number of marbles in Carton A, Carton B and Carton C became 12 : 2 : 1. 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 |
1x4 =
4 u |
2x2 =
4 u |
1 u + 49 |
202 |
| Change |
+ 2x4 =
+ 8 u |
- 1x2 =
- 2 u |
- 49 |
|
| After |
3x4 =
12 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
12 u
|
2 u |
1 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 12 is 12.
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
= 4 u + 4 u + 1 u + 49
= 9 u + 49
9 u + 49 = 202
9 u = 202 - 49
9 u = 153
1 u = 153 ÷ 9 = 17
Number of marbles in Carton C at first
= 1 u + 49
= 1 x 17 + 49
= 17 + 49
= 66
Number of marbles in Carton A and Carton B at first
= 202 - 66
= 136
Carton C : Carton A and Carton B
66 : 136
(÷2)33 : 68
Answer(s): 33 : 68
