Three cartons, A, B and C, contained 242 marbles. Reggie 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 34 marbles from Carton C. As a result, the ratio of the number of marbles in Carton A, Carton B and Carton C became 6 : 4 : 3. 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 |
2x4 = 8 u |
3 u + 34 |
242 |
Change |
+ 2x2 = + 4 u |
- 1x4 = - 4 u |
- 34 |
|
After |
3x2 = 6 u |
1x4 = 4 u |
|
|
Comparing the 3 cartons |
6 u
|
4 u |
3 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 4 is 4.
Total number of marbles at first
= 2 u + 8 u + 3 u + 34
= 13 u + 34
13 u + 34 = 242
13 u = 242 - 34
13 u = 208
1 u = 208 ÷ 13 = 16
Number of marbles in Carton C at first
= 3 u + 34
= 3 x 16 + 34
= 48 + 34
= 82
Number of marbles in Carton A and Carton B at first
= 242 - 82
= 160
Carton C : Carton A and Carton B
82 : 160
(÷2)41 : 80
Answer(s): 41 : 80