Three cartons, A, B and C, contained 78 marbles. Owen 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 42 marbles into Carton C. As a result, the ratio of the number of marbles in Carton A, Carton B and Carton C became 9 : 2 : 5. 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 |
1x3 =
3 u |
2x2 =
4 u |
5 u - 42 |
78 |
| Change |
+ 2x3 =
+ 6 u |
- 1x2 =
- 2 u |
+ 42 |
|
| After |
3x3 =
9 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
9 u |
2 u |
5 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 9 is 9.
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 2 is 2.
Total number of marbles at first
= 3 u + 4 u + 5 u - 42
= 12 u - 42
12 u - 42 = 78
12 u = 78 + 42
12 u = 120
1 u = 120 ÷ 12 = 10
Number of marbles in Carton B at first
= 4 u
= 4 x 10
= 40
Number of marbles in Carton A and Carton C at first
= 78 - 40
= 38
Carton B : Carton A and Carton C
40 : 38
(÷2)20 : 19
Answer(s): 20 : 19
