document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139505>Question 1139505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I think this is a system of equations question. \r<BR>\n" );
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document.write( "A farmer plants soybeans, corn, and wheat and rotates the planting each year on his 500 acre farm. In a particular year, the profits from his crops were $120 per acre of soybeans, $100 per acre of corn, and $80 per acre of wheat. He plants twice as many acres of corn as soybeans.\r<BR>\n" );
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document.write( "How many acres did he plant with each crop the year he made a total profit of $51,000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #759971 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=759971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "It COULD be a system of equations problem; as such, it would be a good exercise in solving such problems.<br><BR>\n" );
document.write( "However, it is much easier to solve if you write and solve a single equation using a single variable.<br><BR>\n" );
document.write( "It will take a little extra time to figure out how to write the single equation in a single variable; but solving that single equation will take far less time than solving a system of three equations in three variables.<br><BR>\n" );
document.write( "Here is how you would probably set up the problem using three variables....<br><BR>\n" );
document.write( "Let x = acres of soybeans<BR>\n" );
document.write( "Let y = acres of corn<BR>\n" );
document.write( "Let z = acres of wheat<br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "(1) x+y+z = 500  (the total acreage is 500)<BR>\n" );
document.write( "(2) y = 2x  (twice as many acres of corn as soybeans)<BR>\n" );
document.write( "(3) 120x + 100y + 80z = 51000  (his profit is $51,000)<br><BR>\n" );
document.write( "You would probably replace \"y\" with \"2x\" in (1) and (3) and then use elimination to solve for either x or z, and then proceed from there....<br><BR>\n" );
document.write( "Here is how you could set up the equation using a single variable:<br><BR>\n" );
document.write( "Let x = acres of soybeans<BR>\n" );
document.write( "Then 2x = acres of corn  (twice as many acres of corn as soybeans)<BR>\n" );
document.write( "And (500-3x) = acres of wheat  (the total acreage is 500; 3x of that is corn or soybeans)<br><BR>\n" );
document.write( "Then the single equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%28x%29%2B100%282x%29%2B80%28500-3x%29+=+51000 ALIGN=MIDDLE  ALT=\"120%28x%29%2B100%282x%29%2B80%28500-3x%29+=+51000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120x%2B200x%2B40000-240x+=+51000 ALIGN=MIDDLE  ALT=\"120x%2B200x%2B40000-240x+=+51000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80x+=+11000 ALIGN=MIDDLE  ALT=\"80x+=+11000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+137.5 ALIGN=MIDDLE  ALT=\"x+=+137.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: x=137.5 acres of soybeans; 2x = 275 acres of corn; (500-412.5) = 87.5 acres of wheat </SPAN>\n" );
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