Three cartons, A, B and C, contained 150 beads. Perry 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 added another 90 beads into Carton C. As a result, the ratio of the number of beads in Carton A, Carton B and Carton C became 9 : 3 : 11. What was the ratio of the number of beads in Carton B to the total number of beads in Carton A and Carton C at first? Give the answer in its lowest term.
| |
Carton A |
Carton B |
Carton C |
Total |
| Before |
1x3 =
3 u |
2x3 =
6 u |
11 u - 90 |
150 |
| Change |
+ 2x3 =
+ 6 u |
- 1x3 =
- 3 u |
+ 90 |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
|
|
Comparing the
3 cartons |
9 u |
3 u |
11 u |
|
The number of beads in Carton A in the end is repeated. Make the number of beads in Carton A in the end the same. LCM of 3 and 9 is 9.
The number of beads in Carton B in the end is repeated. 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
= 3 u + 6 u + 11 u - 90
= 20 u - 90
20 u - 90 = 150
20 u = 150 + 90
20 u = 240
1 u = 240 ÷ 20 = 12
Number of beads in Carton B at first
= 6 u
= 6 x 12
= 72
Number of beads in Carton A and Carton C at first
= 150 - 72
= 78
Carton B : Carton A and Carton C
72 : 78
(÷6)12 : 13
Answer(s): 12 : 13
