document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=707095>Question 707095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer buys 100 animals for $100.00. The animals include at least  one cow, one pig, and one chicken, but no other kind. If a cow costs  $5.00, a pig costs $1.00, and a chicken costs $0.50, how many of each  did he buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #435523 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=435523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> w cow ____________$5 each<BR>\n" );
document.write( "p pig ____________$1 each <BR>\n" );
document.write( "n chicken ________$0.50 each\r<BR>\n" );
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document.write( "w+p+n=100, farmer bought 100 animals<BR>\n" );
document.write( "Examining the cost: 5*w+1*p+0.5*n=100, farmer spent 100 dollars\r<BR>\n" );
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document.write( "w>=1, p>=1, n>=1\r<BR>\n" );
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document.write( "By chance, I assumed w=k, just some assumed natural number, and solved the system for p and n.  I only used simple algebra-1 stuff; no matrix operations.  \r<BR>\n" );
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document.write( "Work was then done on system:<BR>\n" );
document.write( "p+0.5n=100-5k<BR>\n" );
document.write( "p+n=100-k\r<BR>\n" );
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document.write( "My initial results were w=k, p=100-9k, n=8k.  <BR>\n" );
document.write( "One of the specifications was that at least one animal of each kind was bought.  I tried k=1 and computed what that would do for w, p, and n.  Good results:  if k=1, then w=1, p=91, and n=8.  Total 100 animals.   </SPAN>\n" );
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