Three cartons, B, C and A, contained 212 marbles. Wesley 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 22 marbles into Carton A. As a result, the ratio of the number of marbles in Carton B, Carton C and Carton A became 6 : 3 : 5. 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 |
1x2 =
2 u |
2x3 =
6 u |
5 u - 22 |
212 |
| Change |
+ 2x2 =
+ 4 u |
- 1x3 =
- 3 u |
+ 22 |
|
| After |
3x2 =
6 u |
1x3 =
3 u |
|
|
Comparing the
3 cartons |
6 u |
3 u |
5 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 6 is 6.
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 3 is 3.
Total number of marbles at first
= 2 u + 6 u + 5 u - 22
= 13 u - 22
13 u - 22 = 212
13 u = 212 + 22
13 u = 234
1 u = 234 ÷ 13 = 18
Number of marbles in Carton C at first
= 6 u
= 6 x 18
= 108
Number of marbles in Carton B and Carton A at first
= 212 - 108
= 104
Carton C : Carton B and Carton A
108 : 104
(÷4)27 : 26
Answer(s): 27 : 26
