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From: jlc@afinitc.UUCP (Gerald Collins)
Newsgroups: net.puzzle
Subject: Re: Horses, Pigs, and Rabbits
Message-ID: <609@afinitc.UUCP>
Date: Wed, 29-May-85 21:23:18 EDT
Article-I.D.: afinitc.609
Posted: Wed May 29 21:23:18 1985
Date-Received: Fri, 31-May-85 04:39:04 EDT
References: <235@ihnet.UUCP>
Organization: Affinitec Corp., St. Louis
Lines: 31

[]

>  < down on the farm >
>  An old puzzle comes to mind.
>  A farmer goes to market, and buys 100 animals for 100 dollars.
>  Horses cost 10 dollars, pigs cost 3 dollars, and rabbits cost 50 cents.
>  How many of each animal did he buy?
>    Karl Dahlke    ihnp4!ihnet!eklhad

These statements work out to the equations:

	10H + 3P + .5R = 100
and   	H + P + R = 100

a little shuffling gives

	6P + R = 200 - 20H
	P + R = 100 - H

subtracting gives:

	5P = 100 - 19H

divide by five gives:

	P = 20 - 19H/5

Therefore the only solutions possible are where H is divisible by 5.
If H = 10 or any number > 10 then P is negative which is impossible.
Therefore H = 0, P = 20, R = 80, and H = 5, P = 1, R = 94 are the only
solutions possible.