document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269374>Question 269374</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer spends $4,000 to obtain 100 head of livestock.Prices are: calves – $120 each; lambs – $50 each; piglets – $25 each. If he purchased at least one animal of each type and fewer than 10 calves, how many lambs did he buy?\r<BR>\n" );
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document.write( "(1) 44 (2) 46 (3) 48 (4) 50 (5) None of the above </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197526 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=197526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=number of calves<BR>\n" );
document.write( "Let y=number of lambs<BR>\n" );
document.write( "And let z=number of piglets<BR>\n" );
document.write( "Now we are told that:<BR>\n" );
document.write( "x+y+z=100---------------------eq1<BR>\n" );
document.write( "120x+50y+25z=4000<BR>\n" );
document.write( "Divide each term by 5 just to deal in smaller numbers<BR>\n" );
document.write( "24x+10y+5z=800----------eq2<BR>\n" );
document.write( "We have only two equations but three unknowns. Hmmmmmmm.<BR>\n" );
document.write( "BUT WE CAN STILL SOLVE IT!!\r<BR>\n" );
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document.write( "Multiply eq1 by 5 and then subtract it from eq2 and we get:<BR>\n" );
document.write( "19x+5y=300----------eq1a<BR>\n" );
document.write( "solve for y<BR>\n" );
document.write( "y=(300-19x)/5---eq1b  Now we have an equation that relates the number of lambs to the number of calves<BR>\n" );
document.write( "We know several things about this problem that will help us solve it:<BR>\n" );
document.write( "(1) We are told that the number of calves,(x),is less than 10<BR>\n" );
document.write( "(2) We know that we can't have a half a calf, a leg of lamb or a piece of pork.  We must deal in whole numbers.<BR>\n" );
document.write( "(3) We can't have negative calves, lambs or piglets.  We must deal in whole, positive numbers.<BR>\n" );
document.write( "We will now solve eq1b by trial and error, starting with x=9.<BR>\n" );
document.write( "x=9        y=(300-171)/5--------------no good not a whole number<BR>\n" );
document.write( "x=8        y=(300-152)/5--------------no good not a whole number<BR>\n" );
document.write( "x=7        y=(300-133)/5--------------no good not a whole number<BR>\n" );
document.write( "x=6        y=(300-114)/5--------------ditto<BR>\n" );
document.write( "x=5--------y=(300--95)/5=41-----------BINGO ---POSSIBLE SOLUTION<BR>\n" );
document.write( "BY INSPECTION WE CAN SEE THAT WHEN x IS 4, 3, 2 OR 1. WE DO NOT GET ANY MORE WHOLE NUMBERS FOR Y<BR>\n" );
document.write( "Now we have the following:<BR>\n" );
document.write( "x=Calves=5<BR>\n" );
document.write( "y=Lambs=41 ----so your answer is \"none of the above\"<BR>\n" );
document.write( "Substitute these values into eq1 and we get<BR>\n" );
document.write( "5+41+z=100<BR>\n" );
document.write( "z=Piglets=54<BR>\n" );
document.write( "Now<BR>\n" );
document.write( "5*120+41*50+54*25=4000<BR>\n" );
document.write( "600+2050+1350<BR>\n" );
document.write( "4000=4000\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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