Three cartons, B, C and A, contained 132 marbles. Andy 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 98 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 : 11. 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 |
11 u - 98 |
132 |
| Change |
+ 2x4 =
+ 8 u |
- 1x4 =
- 4 u |
+ 98 |
|
| After |
3x4 =
12 u |
1x4 =
4 u |
|
|
Comparing the
3 cartons |
12 u |
4 u |
11 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 + 11 u - 98
= 23 u - 98
23 u - 98 = 132
23 u = 132 + 98
23 u = 230
1 u = 230 ÷ 23 = 10
Number of marbles in Carton C at first
= 8 u
= 8 x 10
= 80
Number of marbles in Carton B and Carton A at first
= 132 - 80
= 52
Carton C : Carton B and Carton A
80 : 52
(÷4)20 : 13
Answer(s): 20 : 13
