Three cartons, C, A and B, contained 302 marbles. Elijah 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 removed 81 marbles from Carton B. As a result, the ratio of the number of marbles in Carton C, Carton A and Carton B became 12 : 4 : 1. What was the ratio of the number of marbles in Carton B to the total number of marbles in Carton C and Carton A at first? Give the answer in its lowest term.
|
Carton C |
Carton A |
Carton B |
Total |
Before |
1x4 = 4 u |
2x4 = 8 u |
1 u + 81 |
302 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
- 81 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 cartons |
12 u
|
4 u |
1 u |
|
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 3 and 12 is 12.
The number of marbles in Carton A in the end is the same. Make the number of marbles in Carton A in the end the same. LCM of 1 and 4 is 4.
Total number of marbles at first
= 4 u + 8 u + 1 u + 81
= 13 u + 81
13 u + 81 = 302
13 u = 302 - 81
13 u = 221
1 u = 221 ÷ 13 = 17
Number of marbles in Carton B at first
= 1 u + 81
= 1 x 17 + 81
= 17 + 81
= 98
Number of marbles in Carton C and Carton A at first
= 302 - 98
= 204
Carton B : Carton C and Carton A
98 : 204
(÷2)49 : 102
Answer(s): 49 : 102