# Week 1 Problem E

## Week 1 Problem E

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

workin on it............ill post my solution later.

**Mira Holford**- The Cool Cube
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## Re: Week 1 Problem E

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.

**Archis**- Admin
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## Re: Week 1 Problem E

wow your good archis!

**Steve**- The Cool Cube
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## Re: Week 1 Problem E

Steve wrote:wow your good archis!

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

**Mira Holford**- The Cool Cube
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