Three cartons, C, A and B, contained 304 marbles. Vincent 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 16 marbles from Carton B. As a result, the ratio of the number of marbles in Carton C, Carton A and Carton B became 9 : 2 : 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 |
1x3 =
3 u |
2x2 =
4 u |
11 u + 16 |
304 |
| Change |
+ 2x3 =
+ 6 u |
- 1x2 =
- 2 u |
- 16 |
|
| After |
3x3 =
9 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
9 u
|
2 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 9 is 9.
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 2 is 2.
Total number of marbles at first
= 3 u + 4 u + 11 u + 16
= 18 u + 16
18 u + 16 = 304
18 u = 304 - 16
18 u = 288
1 u = 288 ÷ 18 = 16
Number of marbles in Carton B at first
= 11 u + 16
= 11 x 16 + 16
= 176 + 16
= 192
Number of marbles in Carton C and Carton A at first
= 304 - 192
= 112
Carton B : Carton C and Carton A
192 : 112
(÷16)12 : 7
Answer(s): 12 : 7
