document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164209>Question 1164209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Susan cashed a check at the bank, but the teller made a mistake. He gave her as many dollars as he should have given her cents and as many cents as he should have given her dollars.  Susan took the money without realizing the error and spent $3.50. She then had twice as much money as the actual amount of the check. What was the amount of the check? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788743 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52811)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788743\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "For linear &nbsp;Diophantine equations &nbsp;(one equation with integer coefficients for two integer unknowns) &nbsp;the trial an error method \r<BR>\n" );
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document.write( "finding a solution is absolutely and totally &nbsp;LEGAL &nbsp;(and standard) &nbsp;method.\r<BR>\n" );
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document.write( "For such equations, &nbsp;any version of trial and error search is &nbsp;ALLOWABLE, &nbsp;and nobody of mature mathematicians \r<BR>\n" );
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document.write( "do not really care by &nbsp;WHICH &nbsp;concretely searching method the solution is obtained.\r<BR>\n" );
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document.write( "You may use an &nbsp;Excel table/spreadsheet for it and to find the solution in seconds &nbsp;(as I usually do it . . . )\r<BR>\n" );
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document.write( "Nobody cares about it . . . \r<BR>\n" );
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document.write( "Or, &nbsp;alternatively, &nbsp;you can find it via &nbsp;30 &nbsp;lines formula transformations. &nbsp;&nbsp;It is also good,\r<BR>\n" );
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document.write( "but again, &nbsp;NOBODY CARES about it . . . \r<BR>\n" );
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document.write( "What is &nbsp;REALLY &nbsp;IMPORTANT &nbsp;for such equations, &nbsp;it is the necessary and sufficient condition for &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28existing%29 ALIGN=MIDDLE  ALT=\"highlight%28existing%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;the solution.\r<BR>\n" );
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document.write( "This condition &nbsp;REQUIRES &nbsp;that the right side constant term must be a MULTIPLE of the Greatest Common Divisor of the coefficients\r<BR>\n" );
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document.write( "of the equation at &nbsp;\"x\" &nbsp;and &nbsp;\"y\".\r<BR>\n" );
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document.write( "If this condition is satisfied, &nbsp;then the solution &nbsp;DOES EXIST, &nbsp;and all the troubles just do stop at this point.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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