document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=223231>Question 223231</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need a real-world example when the solution of a system of linear equations must be in the first quadrant. What do I need to know? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #166955 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=166955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need a real-world example when the solution of a system of linear equations must be in the first quadrant. What do I need to know?\r<BR>\n" );
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document.write( "Here's an example:\r<BR>\n" );
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document.write( "Donnie has $5.10 in nickels, dimes, and quarters.  He has an equal number of dimes and nickels, with the value of the quarters being $2.40 more than the total value of the dimes and nickels.  How many dimes does he have?\r<BR>\n" );
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document.write( "Step 1.  Let x be the number of nickels\r<BR>\n" );
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document.write( "Step 2.  Let x be the number of dimes since they are equal in number with the nickels.\r<BR>\n" );
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document.write( "Step 3.  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.05%2B0.10%29x=0.15x ALIGN=MIDDLE  ALT=\"%280.05%2B0.10%29x=0.15x\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the dollar values of nickels and dimes.\r<BR>\n" );
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document.write( "Step 4.  Let 0.25y be the dollar values of quarters.\r<BR>\n" );
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document.write( "Step 5.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.40%2B0.15x=0.25y ALIGN=MIDDLE  ALT=\"2.40%2B0.15x=0.25y\"   DISABLED_style= \"max-width:90%; height:auto;\" > since the value of the quarters being $2.40 more than the total value of the dimes and nickels.  Or rewriting it as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.15x%2B0.25y=2.40 ALIGN=MIDDLE  ALT=\"-0.15x%2B0.25y=2.40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x%2B0.25y=5.10 ALIGN=MIDDLE  ALT=\"0.15x%2B0.25y=5.10\"   DISABLED_style= \"max-width:90%; height:auto;\" > as given by the problem since $5.10 in nickels, dimes, and quarters.\r<BR>\n" );
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document.write( "Step 7.  Now, we have a linear system of equations in Steps 5 and 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.15x%2B0.25y=2.40 ALIGN=MIDDLE  ALT=\"-0.15x%2B0.25y=2.40\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x%2B0.25y=5.10 ALIGN=MIDDLE  ALT=\"0.15x%2B0.25y=5.10\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Equation B\r<BR>\n" );
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document.write( "Adding Equations A and B\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.15x%2B0.15x%2B0.25y%2B0.25y=2.40%2B5.10 ALIGN=MIDDLE  ALT=\"-0.15x%2B0.15x%2B0.25y%2B0.25y=2.40%2B5.10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.50y=7.50 ALIGN=MIDDLE  ALT=\"0.50y=7.50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15 ALIGN=MIDDLE  ALT=\"y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarters\r<BR>\n" );
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document.write( "Then solving x from Equation B is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.10-3.75=0.15x ALIGN=MIDDLE  ALT=\"5.10-3.75=0.15x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Check Equation A if true <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.15x%2B0.25y=2.40 ALIGN=MIDDLE  ALT=\"-0.15x%2B0.25y=2.40\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.35%2B3.75=2.40 ALIGN=MIDDLE  ALT=\"-1.35%2B3.75=2.40\"   DISABLED_style= \"max-width:90%; height:auto;\" >...which is a true statement.\r<BR>\n" );
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document.write( "Step 8.  ANSWER:  The number of nickels and dimes is 9 each and the number of quarters is 15.\r<BR>\n" );
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document.write( "I hope the above steps were helpful.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( " </SPAN>\n" );
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