Three cartons, A, B and C, contained 340 beads. Sam 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 88 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 : 9. 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 |
9 u + 88 |
340 |
Change |
+ 2x4 = + 8 u |
- 1x4 = - 4 u |
- 88 |
|
After |
3x4 = 12 u |
1x4 = 4 u |
|
|
Comparing the 3 cartons |
12 u
|
4 u |
9 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 + 9 u + 88
= 21 u + 88
21 u + 88 = 340
21 u = 340 - 88
21 u = 252
1 u = 252 ÷ 21 = 12
Number of beads in Carton C at first
= 9 u + 88
= 9 x 12 + 88
= 108 + 88
= 196
Number of beads in Carton A and Carton B at first
= 340 - 196
= 144
Carton C : Carton A and Carton B
196 : 144
(÷4)49 : 36
Answer(s): 49 : 36