Three cartons, B, C and A, contained 218 beads. Ian added some beads into Carton B and the number of beads in Carton B tripled. He took out half of the number of beads from Carton C and added another 48 beads into Carton A. As a result, the ratio of the number of beads in Carton B, Carton C and Carton A became 9 : 2 : 7. What was the ratio of the number of beads in Carton C to the total number of beads in Carton B and Carton A at first? Give the answer in its lowest term.
| |
Carton B |
Carton C |
Carton A |
Total |
| Before |
1x3 =
3 u |
2x2 =
4 u |
7 u - 48 |
218 |
| Change |
+ 2x3 =
+ 6 u |
- 1x2 =
- 2 u |
+ 48 |
|
| After |
3x3 =
9 u |
1x2 =
2 u |
|
|
Comparing the
3 cartons |
9 u |
2 u |
7 u |
|
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 3 and 9 is 9.
The number of beads in Carton C in the end is repeated. Make the number of beads in Carton C in the end the same. LCM of 1 and 2 is 2.
Total number of beads at first
= 3 u + 4 u + 7 u - 48
= 14 u - 48
14 u - 48 = 218
14 u = 218 + 48
14 u = 266
1 u = 266 ÷ 14 = 19
Number of beads in Carton C at first
= 4 u
= 4 x 19
= 76
Number of beads in Carton B and Carton A at first
= 218 - 76
= 142
Carton C : Carton B and Carton A
76 : 142
(÷2)38 : 71
Answer(s): 38 : 71
