document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=9449>Question 9449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello-<BR>\n" );
document.write( "Thanks in advance for helping me with this problem.  I found the answer, but through guess and check, so it would be very helpful if you could tell me how to find the answer mathematicaly.\r<BR>\n" );
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document.write( "Mark and David both own a lot of Matchbox cars.  Mark owns seven times the square root of the amount David owns.  Together they own the square root of 9 multiplyed be the quotient of 27,150 and 181.  How many cars do they own in all?  How many cars does each boy own?  Who owns more?\r<BR>\n" );
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document.write( "This really stumped me, but I found an answer.\r<BR>\n" );
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document.write( "Mark owns 126 cars.<BR>\n" );
document.write( "David owns 324 cars.<BR>\n" );
document.write( "Together they own 450 cars.<BR>\n" );
document.write( "David owns more.\r<BR>\n" );
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document.write( "Thanks again in advance and I can't wait to hear from you.\r<BR>\n" );
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document.write( "Sincerely,<BR>\n" );
document.write( "Trevor Pierce </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5176 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=5176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = number of cars owned by David<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Asqrt%28x%29+ ALIGN=MIDDLE  ALT=\"7%2Asqrt%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number Mark owns.\r<BR>\n" );
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document.write( "Now, the quotient of 29150/181 is just blowing smoke on you.  That would be 150, and the square root of 9 (more smoke!!) is 3, so the total cars owned is 150*3 or 450\r<BR>\n" );
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document.write( "So, finally, here is the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+7+sqrt%28x%29+=+450 ALIGN=MIDDLE  ALT=\"x+%2B+7+sqrt%28x%29+=+450\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To solve a radical equation, which this is, you msut isolate the radical term by subtracting x from each side of the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7sqrt%28x%29+=+450+-+x+ ALIGN=MIDDLE  ALT=\"7sqrt%28x%29+=+450+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, square both sides--that is,  square the entire sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287sqrt%28x%29%29%5E2+=+%28450+-+x%29%5E2 ALIGN=MIDDLE  ALT=\"%287sqrt%28x%29%29%5E2+=+%28450+-+x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49x+=+450%5E2+-+900x+%2B+x%5E2+ ALIGN=MIDDLE  ALT=\"49x+=+450%5E2+-+900x+%2B+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2+-+900x+%2B+202500 ALIGN=MIDDLE  ALT=\"0+=+x%5E2+-+900x+%2B+202500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The numbers here are so large, that you could hardly hope to begin to factor it, although I suspect it DOES factor.  You can use the quadratic formula to solve it, or use the pluggable solver by Igor Chudov, the owner of this website.  \r<BR>\n" );
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document.write( "I'll try the pluggable solver.  The graph is not important here, only the solution to the equation.\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-949x%2B202500+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-949x%2B202500+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-949%29%5E2-4%2A1%2A202500=90601 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-949%29%5E2-4%2A1%2A202500=90601\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=90601 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--949%2B-sqrt%28+90601+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--949%2B-sqrt%28+90601+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-949%29%2Bsqrt%28+90601+%29%29%2F2%5C1+=+625 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-949%29%2Bsqrt%28+90601+%29%29%2F2%5C1+=+625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-949%29-sqrt%28+90601+%29%29%2F2%5C1+=+324 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-949%29-sqrt%28+90601+%29%29%2F2%5C1+=+324\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-949x%2B202500 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-949x%2B202500\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-949x%2B202500+=+1%28x-625%29%2A%28x-324%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-949x%2B202500+=+1%28x-625%29%2A%28x-324%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 625, 324.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-949%2Ax%2B202500+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-949%2Ax%2B202500+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Notice that the equation DOES factor, and the solutions are 625 and 324.  The 625 is more cars than the total, so it must be rejected.  That means that David has 324 cars, and Mark has 450 - x = 126 cars.\r<BR>\n" );
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document.write( "Good problem.  There must be an easier way to solve it.  Maybe someone will find it.\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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