document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=943931>Question 943931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tom has a $20 bill, a $10 bill, a $5 bill, and $1 bill. List the total costs possible for items he could buy if he receives no change. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575578 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=575578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cost, in $, of an item that could be purchased receiving no change is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20a%2B10b%2B5c%2B1d ALIGN=MIDDLE  ALT=\"20a%2B10b%2B5c%2B1d\"   DISABLED_style= \"max-width:90%; height:auto;\" > where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means 2 choices for each variable, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2A2%2A2=2%5E4=16 ALIGN=MIDDLE  ALT=\"2%2A2%2A2%2A2=2%5E4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > choices overall.<BR>\n" );
document.write( "One of those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > choices is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "I suppose $0 would mean not buying anything,<BR>\n" );
document.write( "so if some amount was paid,<BR>\n" );
document.write( "it has to be one of the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16-1=highlight%2815%29 ALIGN=MIDDLE  ALT=\"16-1=highlight%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible amounts.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Now that I know there are 15, I list the amounts,<BR>\n" );
document.write( "and count them to make sure I do not forget any:<BR>\n" );
document.write( "With a $1 bill (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ):<BR>\n" );
document.write( "$1,<BR>\n" );
document.write( "and if we also add a $5 bill (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=1%2Cb=1%29 ALIGN=MIDDLE  ALT=\"system%28a=1%2Cb=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ),<BR>\n" );
document.write( "$1+$5=$6<BR>\n" );
document.write( "$1+$5+$10=$16<BR>\n" );
document.write( "$1+$5+$10+$20=$36<BR>\n" );
document.write( "$1+$5+$20=$26<BR>\n" );
document.write( "With a $1 bill, and a $10 bill, but no $5 bill (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=1%2Cb=0%2Cc=1%29%29 ALIGN=MIDDLE  ALT=\"system%28a=1%2Cb=0%2Cc=1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ),<BR>\n" );
document.write( "$1+$10=$11<BR>\n" );
document.write( "$1+$10+$20=$31<BR>\n" );
document.write( "With a $1 bill, and another bill, but no $5 or $10 bill,<BR>\n" );
document.write( "$1+$20=$21<BR>\n" );
document.write( "With no $1 bill <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ), but including one $5 bill ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ):<BR>\n" );
document.write( "$5<BR>\n" );
document.write( "$5+$10=$15<BR>\n" );
document.write( "$5+$10+$20=$35<BR>\n" );
document.write( "$5+$20=$25<BR>\n" );
document.write( "If no $1 or $5 bill is used ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b=0 ALIGN=MIDDLE  ALT=\"a=b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ):<BR>\n" );
document.write( "$10<BR>\n" );
document.write( "$10+$20=$30<BR>\n" );
document.write( "$20 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );