Three cartons, B, C and A, contained 304 marbles. Michael 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 removed 31 marbles from Carton A. As a result, the ratio of the number of marbles in Carton B, Carton C and Carton A became 6 : 4 : 11. What was the ratio of the number of marbles in Carton A to the total number of marbles in Carton B and Carton C at first? Give the answer in its lowest term.
| |
Carton B |
Carton C |
Carton A |
Total |
| Before |
1x2 =
2 u |
2x4 =
8 u |
11 u + 31 |
304 |
| Change |
+ 2x2 =
+ 4 u |
- 1x4 =
- 4 u |
- 31 |
|
| After |
3x2 =
6 u |
1x4 =
4 u |
|
|
Comparing the
3 cartons |
6 u
|
4 u |
11 u |
|
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 3 and 6 is 6.
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 1 and 4 is 4.
Total number of marbles at first
= 2 u + 8 u + 11 u + 31
= 21 u + 31
21 u + 31 = 304
21 u = 304 - 31
21 u = 273
1 u = 273 ÷ 21 = 13
Number of marbles in Carton A at first
= 11 u + 31
= 11 x 13 + 31
= 143 + 31
= 174
Number of marbles in Carton B and Carton C at first
= 304 - 174
= 130
Carton A : Carton B and Carton C
174 : 130
(÷2)87 : 65
Answer(s): 87 : 65
