document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=326597>Question 326597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $180 of her medical bills, plus 40% of the rest. Under plan B, Giselle would pay the first $220, but only 30% of the rest. For what amount of medical bills will plan B save Giselle Money. Assume she has over $220 in bills. \r<BR>\n" );
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document.write( "Please help I don't understand at all....Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #233838 by </B><A HREF=/tutors/aboutme.mpl?userid=alanc><B>alanc(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alanc><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=alanc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=233838\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Say we denote medical bill by  M.  we don't know what M is.\r<BR>\n" );
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document.write( "The amount Giselle pays is P.   So  in plan A.  P = .4*(M - 180) + 180  because Giselle has to pay $180 and 40% of M- 180  if M > 180.<BR>\n" );
document.write( "or P = M if M <= 180\r<BR>\n" );
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document.write( "In plan B  P = .3*(M - 220) + 220  if M > 220   else P = M   if M <= 220\r<BR>\n" );
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document.write( "We have two equations:   P1 = .4*(M-180) + 180<BR>\n" );
document.write( "                         P2 = .3*(M-220) + 220\r<BR>\n" );
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document.write( "Given M > 220  we want to find out if P1 > P2 or not.\r<BR>\n" );
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document.write( "P1 = .4M + 108<BR>\n" );
document.write( "P2 = .3M + 154\r<BR>\n" );
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document.write( "intersection:  .4M + 108 = .3M + 154\r<BR>\n" );
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document.write( ".1M = 46\r<BR>\n" );
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document.write( "M = 460  P = 292\r<BR>\n" );
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document.write( "Test for M = 220<BR>\n" );
document.write( "P1 = 196 and P2 = 220,  P1 < P2\r<BR>\n" );
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document.write( "Test M = 480 P1 = 300  and P2 = 298, P1 > P2\r<BR>\n" );
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document.write( "So  for   220 <= M <= 460  P1 < P2  Plan A is cheaper than Plan B<BR>\n" );
document.write( "However if  Medical Bills M > 460  then Plan B is cheaper than Plan A. \r<BR>\n" );
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