Three cartons, A, B and C, contained 122 marbles. Harry added some marbles into Carton A and the number of marbles in Carton A tripled. He took out half of the number of marbles from Carton B and added another 87 marbles into Carton C. As a result, the ratio of the number of marbles in Carton A, Carton B and Carton C became 12 : 2 : 11. What was the ratio of the number of marbles in Carton B to the total number of marbles in Carton A and Carton C at first? Give the answer in its lowest term.
|
Carton A |
Carton B |
Carton C |
Total |
Before |
1x4 = 4 u |
2x2 = 4 u |
11 u - 87 |
122 |
Change |
+ 2x4 = + 8 u |
- 1x2 = - 2 u |
+ 87 |
|
After |
3x4 = 12 u |
1x2 = 2 u |
|
|
Comparing the 3 cartons |
12 u |
2 u |
11 u |
|
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 3 and 12 is 12.
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 1 and 2 is 2.
Total number of marbles at first
= 4 u + 4 u + 11 u - 87
= 19 u - 87
19 u - 87 = 122
19 u = 122 + 87
19 u = 209
1 u = 209 ÷ 19 = 11
Number of marbles in Carton B at first
= 4 u
= 4 x 11
= 44
Number of marbles in Carton A and Carton C at first
= 122 - 44
= 78
Carton B : Carton A and Carton C
44 : 78
(÷2)22 : 39
Answer(s): 22 : 39