Three cartons, B, C and A, contained 264 marbles. Ahmad 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 removed 69 marbles from Carton A. As a result, the ratio of the number of marbles in Carton B, Carton C and Carton A became 12 : 2 : 5. What was the ratio of the number of marbles in Carton A to the total number of marbles in Carton B and Carton C at first? Give the answer in its lowest term.
| |
Carton B |
Carton C |
Carton A |
Total |
| Before |
1x4 =
4 u |
2x2 =
4 u |
5 u + 69 |
264 |
| Change |
+ 2x4 =
+ 8 u |
- 1x2 =
- 2 u |
- 69 |
|
| After |
3x4 =
12 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
12 u
|
2 u |
5 u |
|
The number of marbles in Carton B in the end is the same. 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 the same. Make the number of marbles in Carton C in the end the same. LCM of 1 and 2 is 2.
Total number of marbles at first
= 4 u + 4 u + 5 u + 69
= 13 u + 69
13 u + 69 = 264
13 u = 264 - 69
13 u = 195
1 u = 195 ÷ 13 = 15
Number of marbles in Carton A at first
= 5 u + 69
= 5 x 15 + 69
= 75 + 69
= 144
Number of marbles in Carton B and Carton C at first
= 264 - 144
= 120
Carton A : Carton B and Carton C
144 : 120
(÷24)6 : 5
Answer(s): 6 : 5
