document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026238>Question 1026238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A test is worth 200 points.Th test consist of true and false questions worth 6 points each and multiple choice questions are worth 13 points each.how many multiple choice questions are on the test and true and false questions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641470 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a linear Diophantine equation given by 6x + 13y = 200, where x = # of true or false questions, and y = # multiple choice questions. \r<BR>\n" );
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document.write( "A particular solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B0%5D+=+16 ALIGN=MIDDLE  ALT=\"x%5B0%5D+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B0%5D+=+8 ALIGN=MIDDLE  ALT=\"y%5B0%5D+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "All solutions are given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+x%5B0%5D%2B13n=16%2B13n ALIGN=MIDDLE  ALT=\"x+=+x%5B0%5D%2B13n=16%2B13n\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=y%5B0%5D-6n+=+8-6n ALIGN=MIDDLE  ALT=\"y=y%5B0%5D-6n+=+8-6n\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where n is any integer.\r<BR>\n" );
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document.write( "==> There are three possible solutions:\r<BR>\n" );
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document.write( "x = 3, y = 14;<BR>\n" );
document.write( "x = 16, y = 18;<BR>\n" );
document.write( "x = 29, y = 2.\r<BR>\n" );
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document.write( "Note:  The solution was made possible by the fact that gcd(6,13) = 1 divides 200. </SPAN>\n" );
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