document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182609>Question 1182609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lia can rent a van for either $90 per day with unlimited mileage or $50 per day with 250 free miles and an extra $.25 for each mile over 250. for what number of miles traveled in one day with the unlimited mileage plan save Lia money? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812701 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> unlimited plan is 90 dollars a day with no additional mileage charge.\r<BR>\n" );
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document.write( "alternate plan is 50 dollars a day with 250 free miles and an extra .25 per mile for any miles above 250.\r<BR>\n" );
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document.write( "the unlimited plan will save money if the alternate plan costs more than 90 dollars total.\r<BR>\n" );
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document.write( "alternate plan starts at 50 dollars with 250 unlimited miles.<BR>\n" );
document.write( "any miles over 250 are charge at .25 per mile.\r<BR>\n" );
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document.write( "alternate plan equation is y = 50 + .25 * (x - 250) where x > 250<BR>\n" );
document.write( "this is compare to 90 dollars for the limited plan.\r<BR>\n" );
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document.write( "replace y with 90 to get:\r<BR>\n" );
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document.write( "90 = 50 + .25 * (x - 250)<BR>\n" );
document.write( "subtract 50 from both sides of the equation to get:<BR>\n" );
document.write( "40 = .25 * (x - 250)<BR>\n" );
document.write( "divide both sides of the equation by .25 to get:<BR>\n" );
document.write( "40/.25 = x - 250<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "160 = x - 250<BR>\n" );
document.write( "add 250 to both sides of the equation to get:<BR>\n" );
document.write( "x = 410\r<BR>\n" );
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document.write( "they should break even when the alternate plan travels 410 miles.<BR>\n" );
document.write( "the cost for the alternate plan would be 50 dollars + .25 * (410 - 250) = 50 + .25 * 160 = 50 + 40 = 90.\r<BR>\n" );
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document.write( "any miles traveled over 410 miles in the alternate plan will make it more expensive than the unlimited plan.\r<BR>\n" );
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document.write( "you can see this from the following graph.\r<BR>\n" );
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document.write( "red is the unlimited plan.<BR>\n" );
document.write( "blue is the alternate plan.<BR>\n" );
document.write( "coordinate points are in (x,y) format.<BR>\n" );
document.write( "x is the number of miles driven.<BR>\n" );
document.write( "y is the total cost.\r<BR>\n" );
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document.write( "unlimited plan cost 90 dollars.<BR>\n" );
document.write( "alternate plan costs 50 dollars when 250 miles have traveled and 90 dollars when 410 miles have traveled.\r<BR>\n" );
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document.write( "anything over 410 miles and the unlimited plan comes out the winner.<BR>\n" );
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