document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143218>Question 143218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A family on vacation booked three different types of rooms at a hotel, a standard, double and a suite at an average price of US$140 per room. if they were to book only the standard and the suite the average price would reduce to US$135. How much does the suite cost? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104212 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=104212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You won't be able to derive a specific answer, because you have three variables and only two defined relatiionships.\r<BR>\n" );
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document.write( "Cost of standard: x<BR>\n" );
document.write( "Cost of double: y<BR>\n" );
document.write( "Cost of suite: z\r<BR>\n" );
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document.write( "Average of the 3 is 140, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%2Bz%29%2F3=140 ALIGN=MIDDLE  ALT=\"%28x%2By%2Bz%29%2F3=140\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Average of standard and suite is 135, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bz%29%2F2=135 ALIGN=MIDDLE  ALT=\"%28x%2Bz%29%2F2=135\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So you can say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=420 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=420\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bz=270 ALIGN=MIDDLE  ALT=\"x%2Bz=270\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=270-z ALIGN=MIDDLE  ALT=\"x=270-z\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270-z%2By%2Bz=420 ALIGN=MIDDLE  ALT=\"270-z%2By%2Bz=420\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is to say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=150 ALIGN=MIDDLE  ALT=\"y=150\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we know the price of a double, but as for the standard and suite, all you know is that they add up to 270.  The standard could be $1 and the suite $269, or the standard could be $90 and the suite $180 -- or any other combination that totals 270.  So all you can say for sure about the cost of the suite is that it is $270 minus the cost of the standard -- whatever it is.\r<BR>\n" );
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document.write( "From a practical point of view, you would expect the suite to be greater than $150.  After all, who would then book a double room if you could get the suite for the same money?  By the same logic, the standard room must be less than $120 otherwise the suite could not be greater than $150.\r<BR>\n" );
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document.write( "So, for the suite, the cost must be an element of the set of all z such that z * 100 is an integer (can't make change smaller than a penny), 150 < z << 270.  (<< means 'a lot less than').  z has to be 'a lot less than' 270, otherwise the hotel would be charging too little for the standard rooms.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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