document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992129>Question 992129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello and thank you for your time. I have reviewed the same question, basically with different numbers, however I am not understanding how they are coming up with the solution. Any help, (especially with explanation) will be much appreciated.\r<BR>\n" );
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document.write( "You are choosing between two health clubs. Club A offers a membership for a fee of $24 plus a monthly fee of $15. Club B offers a membership for a fee of $23 plus a monthly fee of $19. After how many months will the total cost of each health club be the same? What will be the total cost for each club? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611762 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=611762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of month you are paying for a health club.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount (in $) that you pay for the health club.<BR>\n" );
document.write( "For Club A, what you pay can be calculated as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15x%2B24 ALIGN=MIDDLE  ALT=\"y=15x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For example, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > months you pay<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%22%24+15%22=%22%2430%22 ALIGN=MIDDLE  ALT=\"2%2A%22%24+15%22=%22%2430%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > plus the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2424%22 ALIGN=MIDDLE  ALT=\"%22%2424%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > premiership fee,<BR>\n" );
document.write( "for a total (in $) of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2A15%2B24=30%2B24=54 ALIGN=MIDDLE  ALT=\"y=2%2A15%2B24=30%2B24=54\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For Club B, what you pay can be calculated as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=19x%2B23 ALIGN=MIDDLE  ALT=\"y=19x%2B23\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "With the numbers you give, he total cost of each health club will never be the same.<BR>\n" );
document.write( "When you are assigned a problem like this in class, the numbers were calculated so as to give you  reasonable answer, one that is a whole number of months.<BR>\n" );
document.write( "With the numbers you give, if both costs were the same, you would have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19x%2B23=15x%2B24 ALIGN=MIDDLE  ALT=\"19x%2B23=15x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but that equation is only true for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F4 ALIGN=MIDDLE  ALT=\"x=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means that the cost would be the same if you are a member for just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > months.<BR>\n" );
document.write( "However, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be a whole number, because the clubs will nor charge you for fractions of a month.<BR>\n" );
document.write( "If you do not withdraw from the club before the month begins, they will make you pay for the whole month, anyway, even if you tell them you don't want to be a member any more after one day of that month.\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "TO GET A BETTER IDEA OF HOW THIS KIND OF PROBLEM WORKS:<BR>\n" );
document.write( "You can calculate for different values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and make a table showing the cost for both clubs:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C5%2C%28months%29%2Cx%2C1%2C2%2C3%2CClub%2C+A%2C39%2C54%2C69%2CClub%2CB%2C42%2C61%2C80%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You can also make a graph with those numbers, plotting the points, and connecting them with a line:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C4%2C-10%2C90%2Cgrid%281%29%2C%0D%0Ared%28line%280%2C24%2C3.2%2C72%29%29%2C%0D%0Agreen%28line%280%2C23%2C3.2%2C83.8%29%29%2C%0D%0Ared%28circle%281%2C39%2C0.05%29%29%2Cred%28circle%282%2C54%2C0.05%29%29%2Cred%28circle%283%2C69%2C0.05%29%29%2C%0D%0Alocate%282.7%2C65%2Cred%28Club%29%29%2Clocate%283.3%2C65%2Cred%28A%29%29%2C%0D%0Alocate%282.2%2C85%2Cgreen%28Club%29%29%2Clocate%282.8%2C85%2Cgreen%28B%29%29%2C%0D%0Agreen%28circle%281%2C42%2C0.05%29%29%2Cgreen%28circle%282%2C61%2C0.05%29%29%2Cgreen%28circle%283%2C80%2C0.05%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > It is hard to see in the graph, but the lines cross at a point with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F4 ALIGN=MIDDLE  ALT=\"x=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and that (after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > months) is where the cost would be the same for both clubs.\r<BR>\n" );
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document.write( "With the numbers you give, it is obvious that Club B is always more expensive than Club A,<BR>\n" );
document.write( "and that the cost of Club B rises more steeply ($19 per month) compared to Club A ($15 per month). </SPAN>\n" );
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