document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019647>Question 1019647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This diophantine equation seems impossible for me..\r<BR>\n" );
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document.write( "\"A dealer spent $10000 buying cattle, some at $410 each and the rest at $530 each. How many of each sort did she buy?\" \r<BR>\n" );
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document.write( "I made a diophantine equation for this.. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+410x%2B530y=10000+ ALIGN=MIDDLE  ALT=\"+410x%2B530y=10000+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifies to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+41x%2B53x=1000+ ALIGN=MIDDLE  ALT=\"+41x%2B53x=1000+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "i seem to have most trouble when the c is the biggest number in the equation in ax+by=c\r<BR>\n" );
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document.write( "I tried using euclid's algorithm but it doesnt seem to work for me, i think im using it wrong..\r<BR>\n" );
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document.write( "Any help to the question would be helpful.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635611 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=635611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sometimes it is easier to solve a math problem by brute force, especially when the values we expect to get are moderate, positive values.\r<BR>\n" );
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document.write( "By a little trial and error, a particular solution to the Diophantine equation is x = 5 and y = 15.\r<BR>\n" );
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document.write( "(BTW, A Diophantine equation ax+by = c has solutions if and only if gcd(a,b) divides c. If so, it has infinitely many solutions, and any one solution can be used to generate all the other ones.) </SPAN>\n" );
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