document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160772>Question 160772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When young MacDonald was starting his farm a long time ago, cows cost $10 each, pigs cost $3 each, and chickens cost $0.50 each. He purchased at least one of each kind of animal. He paid axactly $100 for exactly 100 animals. How many chickens did he buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118560 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=118560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=number of cows<BR>\n" );
document.write( "y=number of pigs<BR>\n" );
document.write( "z=number of chicks<BR>\n" );
document.write( "Now we are told that:<BR>\n" );
document.write( "x+y+z=100------------------------------eq1<BR>\n" );
document.write( "10x+3y+0.5z=100--------------------------eq2 ($ understood)\r<BR>\n" );
document.write( "\n" );
document.write( "Three unknowns and only two equations which means there will have to be some trial and error and maybe more than one solution.<BR>\n" );
document.write( "Multiply eq2 by 2 (and we get 20x+6y+z=200) and then subtract eq1 from it and we get:<BR>\n" );
document.write( "19x+5y=100 or<BR>\n" );
document.write( "5y=100-19x  divide each side by 5<BR>\n" );
document.write( "y=(100-19x)/5--------------------------eq3\r<BR>\n" );
document.write( "\n" );
document.write( "Now eq3 gives us a relationship between the number of pigs,y, and the number of cows, x.\r<BR>\n" );
document.write( "\n" );
document.write( "What do we know about this problem:<BR>\n" );
document.write( "First, we know that we cannot have a negative cow, pig or cluck--we deal in positive numbers.<BR>\n" );
document.write( "Secondly, we know that we cannot have a fraction of a cow, pig or cluck--we deal in whole numbers.\r<BR>\n" );
document.write( "\n" );
document.write( "Given the above constraints, we immediately see from eq3 that we cannot have more than 5 cows otherwise we start having negative pigs which is a no-no.<BR>\n" );
document.write( "Now lets make a chart for cows and pics\r<BR>\n" );
document.write( "\n" );
document.write( "cows 5--pigs=(100-19*5)/5=1------------------BINGO!!!!<BR>\n" );
document.write( "NOW WE plug these values into eq1 and see if the chicks come out ok:\r<BR>\n" );
document.write( "\n" );
document.write( "5+1+z=100<BR>\n" );
document.write( "z=100-6=94 chicks<BR>\n" );
document.write( "Tis gives us the 100 animals, next we wil see if the dollars work out by plugging these into eq2<BR>\n" );
document.write( "10*5+3*1+94*0.5=100<BR>\n" );
document.write( "50+3+47=100<BR>\n" );
document.write( "100=100<BR>\n" );
document.write( "So, we know that one answer is:<BR>\n" );
document.write( "10 cows<BR>\n" );
document.write( "1  pig<BR>\n" );
document.write( "94 clucks\r<BR>\n" );
document.write( "\n" );
document.write( "There may be other answers, you can check.<BR>\n" );
document.write( "Hope this helps---ptaylor </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );