Three cartons, A, B and C, contained 244 marbles. Asher 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 added another 56 marbles into Carton C. As a result, the ratio of the number of marbles in Carton A, Carton B and Carton C became 6 : 3 : 7. What was the ratio of the number of marbles in Carton B to the total number of marbles in Carton A and Carton C at first? Give the answer in its lowest term.
| |
Carton A |
Carton B |
Carton C |
Total |
| Before |
1x2 =
2 u |
2x3 =
6 u |
7 u - 56 |
244 |
| Change |
+ 2x2 =
+ 4 u |
- 1x3 =
- 3 u |
+ 56 |
|
| After |
3x2 =
6 u |
1x3 =
3 u |
|
|
Comparing the
3 cartons |
6 u |
3 u |
7 u |
|
The number of marbles in Carton A in the end is repeated. 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 repeated. Make the number of marbles in Carton B in the end the same. LCM of 1 and 3 is 3.
Total number of marbles at first
= 2 u + 6 u + 7 u - 56
= 15 u - 56
15 u - 56 = 244
15 u = 244 + 56
15 u = 300
1 u = 300 ÷ 15 = 20
Number of marbles in Carton B at first
= 6 u
= 6 x 20
= 120
Number of marbles in Carton A and Carton C at first
= 244 - 120
= 124
Carton B : Carton A and Carton C
120 : 124
(÷4)30 : 31
Answer(s): 30 : 31
