Three cartons, A, B and C, contained 285 beads. Neave 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 75 beads from Carton C. As a result, the ratio of the number of beads in Carton A, Carton B and Carton C became 12 : 3 : 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 |
2x3 = 6 u |
5 u + 75 |
285 |
Change |
+ 2x4 = + 8 u |
- 1x3 = - 3 u |
- 75 |
|
After |
3x4 = 12 u |
1x3 = 3 u |
|
|
Comparing the 3 cartons |
12 u
|
3 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 3 is 3.
Total number of beads at first
= 4 u + 6 u + 5 u + 75
= 15 u + 75
15 u + 75 = 285
15 u = 285 - 75
15 u = 210
1 u = 210 ÷ 15 = 14
Number of beads in Carton C at first
= 5 u + 75
= 5 x 14 + 75
= 70 + 75
= 145
Number of beads in Carton A and Carton B at first
= 285 - 145
= 140
Carton C : Carton A and Carton B
145 : 140
(÷5)29 : 28
Answer(s): 29 : 28