Week 1 Problem E

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Week 1 Problem E

Post  Archis on Thu Oct 09, 2008 8:31 am

There are three candidates, Al, Bill, and Charlie. Bill has at least one-fifth the number of votes Charlie has, and has at most one-third the number of votes Al has. If the sum of Bill and Charlie's votes is at least 600, what is the least votes Al can get?
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Re: Week 1 Problem E

Post  Mira Holford on Sun Oct 12, 2008 5:27 am

workin on it............ill post my solution later.
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Re: Week 1 Problem E

Post  Archis on Mon Oct 13, 2008 5:54 am

My solution:

Spoiler:
300 is my answer.

Bill + Charlie is greater than or equal to 600.
Bill is greater than or equal to 1/5 of Charlie's votes, but less than 1/3 of Al's votes.

Now since we want the least for Al, imagine as if all the inequalities were all equal signs. Thus we have B+C= 600; B= (1/5)C; B= (1/3)A

Substituting into the first equation, you get (6/5)C= 600 or C=500
With C=500, therefore B is 100.
With B=100, the least Al could be, by the third equation, is 3B or 300.
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Re: Week 1 Problem E

Post  Steve on Mon Oct 13, 2008 6:55 am

wow your good archis!
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Re: Week 1 Problem E

Post  Mira Holford on Mon Oct 13, 2008 8:45 am

Steve wrote:wow your good archis!


I KNOW!!!!!!!!!!!!
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