Stealing Wine
A dishonest servant takes out 3 pints of wine from a barrel and replaces them with the same amount of water. He repeats this theft twice, removing in total 9 pints and replacing them with water. As a result of this swindle, the diluted wine remaining in the barrel lost half of its former strength.
How much wine was in the barrel before the thievery began?
How much wine was in the barrel before the thievery began?
posted by Zaux at
12:37 PM
3 Comments:
A= mass of alcohol
V= volume in barrel
S= concentration of wine i.e. alcohol per volume
Ao=V*So
A1=So*V-So*3
S1=A1/V
A2=S1*V-S1*3
S2=A2/V
A3=S2*V-S2*3
S3=A3/V=0.5*So
A2=So*(V-3)-3/V*So*(V-3)
A3= (So*(V-3)-3/V*So*(V-3))-3/V*[ So*(V-3)-3/V*So*(V-3)]
A3=So*(V-3-3+9/V-3+9/V+9/V-27/V^2)
A3=So*(-9+V+27/V-27/V^2)
A3/V=S3=0.5*So
So/V*(-9+V+27/V-27/V^2)=0.5*So
2*/V*(-9+V+27/V-27/V^2)=1
Multiply both sides by V^3
-18*V^2+2*V^3+54*V-54=V^3
1*V^3-18*V^2+54*V-54=0
Solve for V
V=14.54
Answer:
V=14.54 pints
Hopefully no mistakes
Cam
Cam I've been following you for the last couple of days, given that I am still in high school I probably may some of this later but still your intelligence is outstanding, all I'm asking is how did you do it and is there anyway that I can reach your standards as well.
Manjinder,
Thank you very much for the compliment. I probably don't deserve it.
The only advice I can give you is: work hard, ask lots of questions, and maintain a thirst for knowledge.
Good luck with your studies.
Cam
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