Three cartons, A, B and C, contained 318 beads. John 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 33 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 : 7. 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 |
7 u + 33 |
318 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
- 33 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 cartons |
12 u
|
4 u |
7 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 + 7 u + 33
= 19 u + 33
19 u + 33 = 318
19 u = 318 - 33
19 u = 285
1 u = 285 ÷ 19 = 15
Number of beads in Carton C at first
= 7 u + 33
= 7 x 15 + 33
= 105 + 33
= 138
Number of beads in Carton A and Carton B at first
= 318 - 138
= 180
Carton C : Carton A and Carton B
138 : 180
(÷6)23 : 30
Answer(s): 23 : 30