document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=414458>Question 414458</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A $3.00 toll is charged to cross the bridge from Sanibel Island to mainland Florida. A six-month pass, costing $15.00, reduces the toll to $.50. A one-year pass, costing $150, allows for free crossings. How many crossings per year does it take, on average, for two six-months passes to be the most economical choice? Assume a constant number of trips per month, Show work and explain answer.  \r<BR>\n" );
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document.write( "I am not sure what formula to use for this problem. Please Help! :/ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290723 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=290723\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = crossings per year it takes, on average, for two six-months passes to be the<BR>\n" );
document.write( "most economical choice.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > = cost per year to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > crossings<BR>\n" );
document.write( "Assume a constant number of trips per month<BR>\n" );
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document.write( "Without buying any passes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B1%5D+=+3x ALIGN=MIDDLE  ALT=\"C%5B1%5D+=+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Buying 2 6-month passes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B2%5D+=+.5x+%2B+2%2A15 ALIGN=MIDDLE  ALT=\"C%5B2%5D+=+.5x+%2B+2%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Buying a 1-year pass:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B3%5D+=+150 ALIGN=MIDDLE  ALT=\"C%5B3%5D+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "First I'll set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B1%5D+=+C%5B2%5D ALIGN=MIDDLE  ALT=\"C%5B1%5D+=+C%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find intersection<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+.5x+%2B+2%2A15 ALIGN=MIDDLE  ALT=\"3x+=+.5x+%2B+2%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+.5x+%2B+30 ALIGN=MIDDLE  ALT=\"3x+=+.5x+%2B+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5x+=+30 ALIGN=MIDDLE  ALT=\"2.5x+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12 ALIGN=MIDDLE  ALT=\"x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "12 crossings per year make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B1%5D+=+C%5B2%5D ALIGN=MIDDLE  ALT=\"C%5B1%5D+=+C%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One more crossing, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+13 ALIGN=MIDDLE  ALT=\"x+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, make<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B1%5D+=+3%2A13 ALIGN=MIDDLE  ALT=\"C%5B1%5D+=+3%2A13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B1%5D+=+39 ALIGN=MIDDLE  ALT=\"C%5B1%5D+=+39\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B2%5D+=+.5%2A13+%2B+30 ALIGN=MIDDLE  ALT=\"C%5B2%5D+=+.5%2A13+%2B+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B2%5D+=+36.5 ALIGN=MIDDLE  ALT=\"C%5B2%5D+=+36.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B2%5D ALIGN=MIDDLE  ALT=\"C%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes more economical on the 13th crossing by $2.50<BR>\n" );
document.write( "and it still cost less than the 1-year pass for $150<BR>\n" );
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document.write( "  </SPAN>\n" );
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