Three cartons, A, B and C, contained 246 beads. Ethan added some beads into Carton A and the number of beads in Carton A tripled. He took out half of the number of beads from Carton B and removed 42 beads from Carton C. As a result, the ratio of the number of beads in Carton A, Carton B and Carton C became 12 : 4 : 5. What was the ratio of the number of beads in Carton C to the total number of beads in Carton A and Carton B at first? Give the answer in its lowest term.
| |
Carton A |
Carton B |
Carton C |
Total |
| Before |
1x4 =
4 u |
2x4 =
8 u |
5 u + 42 |
246 |
| Change |
+ 2x4 =
+ 8 u |
- 1x4 =
- 4 u |
- 42 |
|
| After |
3x4 =
12 u |
1x4 =
4 u |
|
|
Comparing the
3 cartons |
12 u
|
4 u |
5 u |
|
The number of beads in Carton A in the end is the same. Make the number of beads in Carton A in the end the same. LCM of 3 and 12 is 12.
The number of beads in Carton B in the end is the same. Make the number of beads in Carton B in the end the same. LCM of 1 and 4 is 4.
Total number of beads at first
= 4 u + 8 u + 5 u + 42
= 17 u + 42
17 u + 42 = 246
17 u = 246 - 42
17 u = 204
1 u = 204 ÷ 17 = 12
Number of beads in Carton C at first
= 5 u + 42
= 5 x 12 + 42
= 60 + 42
= 102
Number of beads in Carton A and Carton B at first
= 246 - 102
= 144
Carton C : Carton A and Carton B
102 : 144
(÷6)17 : 24
Answer(s): 17 : 24
