Three cartons, B, C and A, contained 126 marbles. Ken 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 added another 84 marbles into Carton A. As a result, the ratio of the number of marbles in Carton B, Carton C and Carton A became 6 : 2 : 9. What was the ratio of the number of marbles in Carton C to the total number of marbles in Carton B and Carton A at first? Give the answer in its lowest term.
|
Carton B |
Carton C |
Carton A |
Total |
Before |
1x2 = 2 u |
2x2 = 4 u |
9 u - 84 |
126 |
Change |
+ 2x2 = + 4 u |
- 1x2 = - 2 u |
+ 84 |
|
After |
3x2 = 6 u |
1x2 = 2 u |
|
|
Comparing the 3 cartons |
6 u |
2 u |
9 u |
|
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 3 and 6 is 6.
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 1 and 2 is 2.
Total number of marbles at first
= 2 u + 4 u + 9 u - 84
= 15 u - 84
15 u - 84 = 126
15 u = 126 + 84
15 u = 210
1 u = 210 ÷ 15 = 14
Number of marbles in Carton C at first
= 4 u
= 4 x 14
= 56
Number of marbles in Carton B and Carton A at first
= 126 - 56
= 70
Carton C : Carton B and Carton A
56 : 70
(÷14)4 : 5
Answer(s): 4 : 5