document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005924>Question 1005924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A dept. store in your town charges9.75% tax: the store's location in your cousin<BR>\n" );
document.write( "town only charges 7.75% tax.  If a shopper's pre-tax receipt is between $11.57 and $81.43, write and graph a compound inequality that describes the difference in taxes paid for the two locations. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622391 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=622391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is too bad that the sales tax is as high as 9.75% in your town.<BR>\n" );
document.write( "It would be a good idea to do as much of your buying as possible in your cousin's town.<BR>\n" );
document.write( "If the pre-tax total , in $, of a purchase is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the tax would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0975x ALIGN=MIDDLE  ALT=\"0.0975x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in your town, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0775x ALIGN=MIDDLE  ALT=\"0.0775x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in your cousin's town.<BR>\n" );
document.write( "The difference is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0975x-0.0775x=0.02x ALIGN=MIDDLE  ALT=\"0.0975x-0.0775x=0.02x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "a 2% savings.<BR>\n" );
document.write( "\"The shopper's pre-tax receipt is between $11.57 and $81.43\" translates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.57%3C=x%3C=81.43 ALIGN=MIDDLE  ALT=\"11.57%3C=x%3C=81.43\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is a compound inequality.<BR>\n" );
document.write( "It is called a compound inequality,<BR>\n" );
document.write( "because it is made of two inequalities,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2811.57%3C=x%2Cx%3C=81.43%29 ALIGN=MIDDLE  ALT=\"system%2811.57%3C=x%2Cx%3C=81.43%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , written together.<BR>\n" );
document.write( "If you multiply both sides of an inequality times the same positive number,<BR>\n" );
document.write( "you get an equivalent inequality, and do not need to reverse the inequality.<BR>\n" );
document.write( "So, from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.57%3C=x ALIGN=MIDDLE  ALT=\"11.57%3C=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.02%2A11.57%3C=0.02x ALIGN=MIDDLE  ALT=\"0.02%2A11.57%3C=0.02x\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2314%3C=0.02x ALIGN=MIDDLE  ALT=\"0.2314%3C=0.02x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Applying that to both parts of the compound inequality, you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.57%3C=x%2Cx%3C=81.43 ALIGN=MIDDLE  ALT=\"11.57%3C=x%2Cx%3C=81.43\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.02%2A11.57%3C=0.02x%3C=0.02%2A81.43 ALIGN=MIDDLE  ALT=\"0.02%2A11.57%3C=0.02x%3C=0.02%2A81.43\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2314%3C=0.02x%3C=1.6286 ALIGN=MIDDLE  ALT=\"0.2314%3C=0.02x%3C=1.6286\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "because the total price, and hence the tax, would be rounded to the nearest $0.01,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2314 ALIGN=MIDDLE  ALT=\"0.2314\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be rounded to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.23 ALIGN=MIDDLE  ALT=\"0.23\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6286 ALIGN=MIDDLE  ALT=\"1.6286\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be rounded to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.63 ALIGN=MIDDLE  ALT=\"1.63\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "I would say that the compound inequality expected is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%240.23%3C=savings%3C=%241.63 ALIGN=MIDDLE  ALT=\"%240.23%3C=savings%3C=%241.63\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "maybe with or without the \"$\",<BR>\n" );
document.write( "maybe giving a cute one-letter name to \"savings\".<BR>\n" );
document.write( "A way to graph that would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C150%2C-0.1%2C1.9%2C-0.7%2C0.3%2C%0D%0Aarrow%281%2C0%2C1.9%2C0%29%2C%0D%0Aarrow%281%2C0%2C-0.5%2C0%29%2Cline%280%2C-0.07%2C0%2C0.07%29%2C%0D%0Aline%280.1%2C-0.01%2C0.1%2C0.01%29%2Cline%280.2%2C-0.01%2C0.2%2C0.01%29%2C%0D%0Aline%280.3%2C-0.01%2C0.3%2C0.01%29%2Cline%280.4%2C-0.01%2C0.4%2C0.01%29%2C%0D%0Aline%280.5%2C-0.07%2C0.5%2C0.07%29%2Cline%280.6%2C-0.01%2C0.6%2C0.01%29%2C%0D%0Aline%280.7%2C-0.01%2C0.7%2C0.01%29%2Cline%280.8%2C-0.01%2C0.8%2C0.01%29%2C%0D%0Aline%280.9%2C-0.01%2C0.9%2C0.01%29%2Cline%281%2C-0.07%2C1%2C0.07%29%2C%0D%0Aline%281.1%2C-0.01%2C1.1%2C0.01%29%2Cline%281.2%2C-0.01%2C1.2%2C0.01%29%2C%0D%0Aline%281.3%2C-0.01%2C1.3%2C0.01%29%2Cline%281.4%2C-0.01%2C1.4%2C0.01%29%2C%0D%0Aline%281.5%2C-0.07%2C1.5%2C0.07%29%2Cline%281.6%2C-0.01%2C1.6%2C0.01%29%2C%0D%0Aline%281.7%2C-0.01%2C1.7%2C0.01%29%2Cline%281.8%2C-0.01%2C1.8%2C0.01%29%2C%0D%0Alocate%28-0.1%2C-0.07%2C%220.00%22%29%2Clocate%280.4%2C-0.07%2C%220.50%22%29%2C%0D%0Alocate%280.9%2C-0.07%2C%221.00%22%29%2Clocate%281.4%2C-0.07%2C1.50%29%2C%0D%0Ared%28line%280.23%2C0%2C1.63%2C0%29%29%2Clocate%280.13%2C-0.5%2C0.23%29%2C%0D%0Aarrow%280.23%2C-0.5%2C0.23%2C-0.02%29%2Clocate%281.53%2C-0.5%2C1.63%29%2C%0D%0Aarrow%281.63%2C-0.5%2C1.63%2C-0.02%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "I assume something like that is what was expected,<BR>\n" );
document.write( "but different teachers have different format preferences,<BR>\n" );
document.write( "and different ways to fuzzily explain what they want.<BR>\n" );
document.write( "It is sometimes hard to guess what the teacher expects,<BR>\n" );
document.write( "even if you have been in class, paying attention.<BR>\n" );
document.write( "Good luck! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );