Three cartons, B, C and A, contained 206 marbles. Zeph 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 79 marbles into Carton A. As a result, the ratio of the number of marbles in Carton B, Carton C and Carton A became 12 : 4 : 7. 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 |
1x4 = 4 u |
2x4 = 8 u |
7 u - 79 |
206 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
+ 79 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 cartons |
12 u |
4 u |
7 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 12 is 12.
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 4 is 4.
Total number of marbles at first
= 4 u + 8 u + 7 u - 79
= 19 u - 79
19 u - 79 = 206
19 u = 206 + 79
19 u = 285
1 u = 285 ÷ 19 = 15
Number of marbles in Carton C at first
= 8 u
= 8 x 15
= 120
Number of marbles in Carton B and Carton A at first
= 206 - 120
= 86
Carton C : Carton B and Carton A
120 : 86
(÷2)60 : 43
Answer(s): 60 : 43