Three cartons, C, A and B, contained 178 marbles. Dylan 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 14 marbles into Carton B. As a result, the ratio of the number of marbles in Carton C, Carton A and Carton B became 9 : 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 |
1x3 = 3 u |
2x3 = 6 u |
7 u - 14 |
178 |
Change |
+ 2x3 = + 6 u |
- 1x3 = - 3 u |
+ 14 |
|
After |
3x3 = 9 u |
1x3 = 3 u |
|
|
Comparing the 3 cartons |
9 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 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 3 is 3.
Total number of marbles at first
= 3 u + 6 u + 7 u - 14
= 16 u - 14
16 u - 14 = 178
16 u = 178 + 14
16 u = 192
1 u = 192 ÷ 16 = 12
Number of marbles in Carton A at first
= 6 u
= 6 x 12
= 72
Number of marbles in Carton C and Carton B at first
= 178 - 72
= 106
Carton A : Carton C and Carton B
72 : 106
(÷2)36 : 53
Answer(s): 36 : 53