Three cartons, C, A and B, contained 171 marbles. Glen 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 16 marbles into Carton B. As a result, the ratio of the number of marbles in Carton C, Carton A and Carton B became 12 : 3 : 7. 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 |
1x4 = 4 u |
2x3 = 6 u |
7 u - 16 |
171 |
Change |
+ 2x4 = + 8 u |
- 1x3 = - 3 u |
+ 16 |
|
After |
3x4 = 12 u |
1x3 = 3 u |
|
|
Comparing the 3 cartons |
12 u |
3 u |
7 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 12 is 12.
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 3 is 3.
Total number of marbles at first
= 4 u + 6 u + 7 u - 16
= 17 u - 16
17 u - 16 = 171
17 u = 171 + 16
17 u = 187
1 u = 187 ÷ 17 = 11
Number of marbles in Carton A at first
= 6 u
= 6 x 11
= 66
Number of marbles in Carton C and Carton B at first
= 171 - 66
= 105
Carton A : Carton C and Carton B
66 : 105
(÷3)22 : 35
Answer(s): 22 : 35