Three cartons, C, A and B, contained 185 beads. Howard added some beads into Carton C and the number of beads in Carton C tripled. He took out half of the number of beads from Carton A and removed 25 beads from Carton B. As a result, the ratio of the number of beads in Carton C, Carton A and Carton B became 9 : 2 : 9. What was the ratio of the number of beads in Carton B to the total number of beads in Carton C and Carton A at first? Give the answer in its lowest term.
|
Carton C |
Carton A |
Carton B |
Total |
Before |
1x3 = 3 u |
2x2 = 4 u |
9 u + 25 |
185 |
Change |
+ 2x3 = + 6 u |
- 1x2 = - 2 u |
- 25 |
|
After |
3x3 = 9 u |
1x2 = 2 u |
|
|
Comparing the 3 cartons |
9 u
|
2 u |
9 u |
|
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 3 and 9 is 9.
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 1 and 2 is 2.
Total number of beads at first
= 3 u + 4 u + 9 u + 25
= 16 u + 25
16 u + 25 = 185
16 u = 185 - 25
16 u = 160
1 u = 160 ÷ 16 = 10
Number of beads in Carton B at first
= 9 u + 25
= 9 x 10 + 25
= 90 + 25
= 115
Number of beads in Carton C and Carton A at first
= 185 - 115
= 70
Carton B : Carton C and Carton A
115 : 70
(÷5)23 : 14
Answer(s): 23 : 14