Three cartons, B, C and A, contained 301 marbles. Fabian 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 9 : 2 : 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 |
1x3 = 3 u |
2x2 = 4 u |
11 u + 31 |
301 |
Change |
+ 2x3 = + 6 u |
- 1x2 = - 2 u |
- 31 |
|
After |
3x3 = 9 u |
1x2 = 2 u |
|
|
Comparing the 3 cartons |
9 u
|
2 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 9 is 9.
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 2 is 2.
Total number of marbles at first
= 3 u + 4 u + 11 u + 31
= 18 u + 31
18 u + 31 = 301
18 u = 301 - 31
18 u = 270
1 u = 270 ÷ 18 = 15
Number of marbles in Carton A at first
= 11 u + 31
= 11 x 15 + 31
= 165 + 31
= 196
Number of marbles in Carton B and Carton C at first
= 301 - 196
= 105
Carton A : Carton B and Carton C
196 : 105
(÷7)28 : 15
Answer(s): 28 : 15