document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142728>Question 1142728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bank teller cashes a check for $1500 using a certain number of $1 bills, ten times as many $5 bills, a certain number of $10 bills, and twice as many $50 bills. How many of each did the teller use?\r<BR>\n" );
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document.write( "A = $1\r<BR>\n" );
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document.write( "B = $5\r<BR>\n" );
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document.write( "C = $10\r<BR>\n" );
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document.write( "D = $50\r<BR>\n" );
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document.write( "$1500 = A + 10B + C + D2\r<BR>\n" );
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document.write( "Not sure.  Non-homework.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763468 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13209)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let x be the number of $1 bills; then 10x is the number of $5 bills.<br><BR>\n" );
document.write( "Let y be the number of $10 bills; then 2y is the number of $50 bills.<br><BR>\n" );
document.write( "The total value of the bills is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%28x%29%2B5%2810x%29%2B10%28y%29%2B50%282y%29+=+51x%2B110y ALIGN=MIDDLE  ALT=\"1%28x%29%2B5%2810x%29%2B10%28y%29%2B50%282y%29+=+51x%2B110y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The total value is given as $1500:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51x%2B110y+=+1500 ALIGN=MIDDLE  ALT=\"51x%2B110y+=+1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use some logical reasoning to solve this quickly, knowing that x and y are positive integers (or possibly non-negative integers).<br><BR>\n" );
document.write( "\"110y\" and \"1500\" are both multiples of 10; that means \"51x\" has to be a multiple of 10.  And that of course means x is a multiple of 10.<br><BR>\n" );
document.write( "And trying x=10 gives you a solution in integers, so that is the solution:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51%2810%29%2B110y+=+1500 ALIGN=MIDDLE  ALT=\"51%2810%29%2B110y+=+1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110y%2B510+=+1500 ALIGN=MIDDLE  ALT=\"110y%2B510+=+1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110y+=+990 ALIGN=MIDDLE  ALT=\"110y+=+990\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9 ALIGN=MIDDLE  ALT=\"y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "$1 bills: x = 10<BR>\n" );
document.write( "$5 bills: 10x = 100<BR>\n" );
document.write( "$10 bills: y = 9<BR>\n" );
document.write( "$50 bills: 2y = 18<br.<BR>\n" );
document.write( "CHECK: 10(1)+100(5)+9(10)+18(50) = 10+500+90+900 = 1500 </SPAN>\n" );
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