Three cartons, B, C and A, contained 290 beads. Jenson 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 removed 34 beads from Carton A. As a result, the ratio of the number of beads in Carton B, Carton C and Carton A became 9 : 3 : 7. What was the ratio of the number of beads in Carton A to the total number of beads in Carton B and Carton C at first? Give the answer in its lowest term.
| |
Carton B |
Carton C |
Carton A |
Total |
| Before |
1x3 =
3 u |
2x3 =
6 u |
7 u + 34 |
290 |
| Change |
+ 2x3 =
+ 6 u |
- 1x3 =
- 3 u |
- 34 |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
|
|
Comparing the
3 cartons |
9 u
|
3 u |
7 u |
|
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 3 and 9 is 9.
The number of beads in Carton C in the end is the same. Make the number of beads in Carton C in the end the same. LCM of 1 and 3 is 3.
Total number of beads at first
= 3 u + 6 u + 7 u + 34
= 16 u + 34
16 u + 34 = 290
16 u = 290 - 34
16 u = 256
1 u = 256 ÷ 16 = 16
Number of beads in Carton A at first
= 7 u + 34
= 7 x 16 + 34
= 112 + 34
= 146
Number of beads in Carton B and Carton C at first
= 290 - 146
= 144
Carton A : Carton B and Carton C
146 : 144
(÷2)73 : 72
Answer(s): 73 : 72
