Three cartons, C, A and B, contained 96 marbles. Justin 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 added another 84 marbles into 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 A to the total number of marbles in Carton C and Carton B 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 - 84 |
96 |
Change |
+ 2x3 = + 6 u |
- 1x2 = - 2 u |
+ 84 |
|
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 repeated. 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 repeated. 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 - 84
= 18 u - 84
18 u - 84 = 96
18 u = 96 + 84
18 u = 180
1 u = 180 ÷ 18 = 10
Number of marbles in Carton A at first
= 4 u
= 4 x 10
= 40
Number of marbles in Carton C and Carton B at first
= 96 - 40
= 56
Carton A : Carton C and Carton B
40 : 56
(÷8)5 : 7
Answer(s): 5 : 7