Three cartons, A, B and C, contained 114 beads. Jeremy 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 16 beads into Carton C. As a result, the ratio of the number of beads in Carton A, Carton B and Carton C became 12 : 2 : 5. 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 |
1x4 =
4 u |
2x2 =
4 u |
5 u - 16 |
114 |
| Change |
+ 2x4 =
+ 8 u |
- 1x2 =
- 2 u |
+ 16 |
|
| After |
3x4 =
12 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
12 u |
2 u |
5 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 12 is 12.
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 2 is 2.
Total number of beads at first
= 4 u + 4 u + 5 u - 16
= 13 u - 16
13 u - 16 = 114
13 u = 114 + 16
13 u = 130
1 u = 130 ÷ 13 = 10
Number of beads in Carton B at first
= 4 u
= 4 x 10
= 40
Number of beads in Carton A and Carton C at first
= 114 - 40
= 74
Carton B : Carton A and Carton C
40 : 74
(÷2)20 : 37
Answer(s): 20 : 37
