Three cartons, C, A and B, contained 436 marbles. Seth added some marbles into Carton C and the number of marbles in Carton C tripled. He took out half of the number of marbles from Carton A and removed 58 marbles from Carton B. As a result, the ratio of the number of marbles in Carton C, Carton A and Carton B became 12 : 3 : 11. What was the ratio of the number of marbles in Carton B to the total number of marbles in Carton C and Carton A at first? Give the answer in its lowest term.
| |
Carton C |
Carton A |
Carton B |
Total |
| Before |
1x4 =
4 u |
2x3 =
6 u |
11 u + 58 |
436 |
| Change |
+ 2x4 =
+ 8 u |
- 1x3 =
- 3 u |
- 58 |
|
| After |
3x4 =
12 u |
1x3 =
3 u |
|
|
Comparing the
3 cartons |
12 u
|
3 u |
11 u |
|
The number of marbles in Carton C in the end is the same. Make the number of marbles in Carton C in the end the same. LCM of 3 and 12 is 12.
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 1 and 3 is 3.
Total number of marbles at first
= 4 u + 6 u + 11 u + 58
= 21 u + 58
21 u + 58 = 436
21 u = 436 - 58
21 u = 378
1 u = 378 ÷ 21 = 18
Number of marbles in Carton B at first
= 11 u + 58
= 11 x 18 + 58
= 198 + 58
= 256
Number of marbles in Carton C and Carton A at first
= 436 - 256
= 180
Carton B : Carton C and Carton A
256 : 180
(÷4)64 : 45
Answer(s): 64 : 45
