document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261964>Question 261964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jim,<BR>\n" );
document.write( "   I have tried to follow and plug in the equation but it is not working. I have been at this for over an hour and my brain is fried. Help!!\r<BR>\n" );
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document.write( "Bayside Insurance offers two health plans. Under plan A Giselle would have to pay the first $140 of her bills and 25% of the rest. Under plan B she would have to pay the first $160 of her bills and 20% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $160 in bills.\r<BR>\n" );
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document.write( "Giselle would save with plan B if she had more than $_________in bills?\r<BR>\n" );
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document.write( "When it says assume she has over $160 in bills, does that mean you can use any number higher than 160? \r<BR>\n" );
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document.write( "Please help,<BR>\n" );
document.write( "Thank you<BR>\n" );
document.write( "Deborah </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193054 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The reason why we're assuming that she has over $160 in medical bills is if she had less than $160 in bills, then she would be clearly paying more for plan B. For instance, if she has $159 in bills, then she pays almost $15 more for plan B.\r<BR>\n" );
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document.write( "Let x = amount Giselle has to pay (ie her bill)\r<BR>\n" );
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document.write( "Under plan A, she has to pay the first $140 and then 25% of the rest. So if we assume that she has over $160 in bills, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E160 ALIGN=MIDDLE  ALT=\"x%3E160\"   DISABLED_style= \"max-width:90%; height:auto;\" >. After she pays the initial $140, then she has 25% of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-140 ALIGN=MIDDLE  ALT=\"x-140\"   DISABLED_style= \"max-width:90%; height:auto;\" > in bills left over. So this means that under plan A, the cost is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=140%2B0.25%28x-140%29 ALIGN=MIDDLE  ALT=\"c=140%2B0.25%28x-140%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Similarly, under plan B, because \"she would have to pay the first $160 of her bills and 20% of the rest\", this means that the cost for plan B is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=160%2B0.20%28x-160%29 ALIGN=MIDDLE  ALT=\"c=160%2B0.20%28x-160%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So to figure out when plan B will save her money, simply set the plan B expression less than the plan A expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Plan_B%3CPlan_A ALIGN=MIDDLE  ALT=\"Plan_B%3CPlan_A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160%2B0.20%28x-160%29%3C140%2B0.25%28x-140%29 ALIGN=MIDDLE  ALT=\"160%2B0.20%28x-160%29%3C140%2B0.25%28x-140%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute the given cost equations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160%2B0.20x-32%3C140%2B0.25x-35 ALIGN=MIDDLE  ALT=\"160%2B0.20x-32%3C140%2B0.25x-35\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=128%2B0.20x%3C105%2B0.25x ALIGN=MIDDLE  ALT=\"128%2B0.20x%3C105%2B0.25x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20x-0.25x%3C105-128 ALIGN=MIDDLE  ALT=\"0.20x-0.25x%3C105-128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 0.25x from both sides. Subtract 128 from both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.05x%3C-23 ALIGN=MIDDLE  ALT=\"-0.05x%3C-23\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E460 ALIGN=MIDDLE  ALT=\"x%3E460\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -0.05. Remember that dividing both sides by a negative number will flip the inequality sign.\r<BR>\n" );
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document.write( "So if she has any bills over $460, then Plan B will cost less than Plan A. \r<BR>\n" );
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document.write( "If you're skeptical, try some values of 'x' that are around $460. Try x=400, x=450, x=500 (and maybe more) and you'll notice that plan B will become cheaper after you pass x=450.\r<BR>\n" );
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document.write( "Note: the plans cost the same when the bill is $460. This is cross over point when the plans switch in cost. </SPAN>\n" );
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