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Week 1 Problem E
Archis 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?
Archis- Admin
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Re: Week 1 Problem E
Mira Holford Sun Oct 12, 2008 5:27 am
workin on it............ill post my solution later.
Mira Holford- The Cool Cube
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Re: Week 1 Problem E
Archis 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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Steve- The Cool Cube
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Re: Week 1 Problem E
Mira Holford Mon Oct 13, 2008 8:45 am
Steve wrote:wow your good archis!
I KNOW!!!!!!!!!!!!
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