document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138733>Question 1138733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for <BR>\n" );
document.write( "31<BR>\n" );
document.write( " minutes of calls is <BR>\n" );
document.write( "$18.31<BR>\n" );
document.write( " and the monthly cost for <BR>\n" );
document.write( "87<BR>\n" );
document.write( " minutes is <BR>\n" );
document.write( "$25.03<BR>\n" );
document.write( ". What is the monthly cost for <BR>\n" );
document.write( "86<BR>\n" );
document.write( " minutes of calls?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756538 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=756538\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the monthly cost for 31 minutes is $18.31.\r<BR>\n" );
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document.write( "if there were no fixed monthly charges, the cost per call would be 18.31 / 31 = .59..... per minute.\r<BR>\n" );
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document.write( "the monthly cost for 87 minutes is $25.03.\r<BR>\n" );
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document.write( "if there were no fixed monthly charges, the cost per call would be 25.03 / 87 = .28..... per minute.\r<BR>\n" );
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document.write( "it appears there are some fixed charges per month that need to be accounted for.\r<BR>\n" );
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document.write( "if so, the fixed charges per month would be the same every month and the incremental charges per minute per month would be the same every month.\r<BR>\n" );
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document.write( "if we let f = the fixed charges per month and i equal the incremental charges per month and m equal the number of minutes used per month and c = the total cost per month, then the formula would be:\r<BR>\n" );
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document.write( "c = f + m * i.\r<BR>\n" );
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document.write( "the monthly cost for 31 minutes of calls is $18.31.\r<BR>\n" );
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document.write( "the formula for that becomes 18.31 = f + 31 * i.\r<BR>\n" );
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document.write( "the monthly cost for 87 minutes of calls is $25.03.\r<BR>\n" );
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document.write( "the formula for that becomes 25.03 = f + 87 * i.\r<BR>\n" );
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document.write( "we have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "18.31 = f + 31 * i<BR>\n" );
document.write( "25.03 = f + 87 * i\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "25.03 - 18.31 = f - f + 87 * i - 31 * i\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "6.72 = 56 * i\r<BR>\n" );
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document.write( "solve for i to get i = 6.72 / 56 = .12\r<BR>\n" );
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document.write( "the incremental cost per minute of calls is .12.\r<BR>\n" );
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document.write( "take any one of the two original equations and replace i with .12 to solve for f.\r<BR>\n" );
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document.write( "18.31 = f + 31 * i becomes 18.31 = f + 31 * .12 which becomes 18.31 = f + 3.72.\r<BR>\n" );
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document.write( "solve for f to get f = 18.31 - 3.72 = 14.59.\r<BR>\n" );
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document.write( "if we did this right, the fixed cost per month is 14.59 and the incremental cost per minute of calls is .12.\r<BR>\n" );
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document.write( "to confirm, we use these values in the two original equations.\r<BR>\n" );
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document.write( "18.31 = f + 31 * i becomes 18.31 = 14.59 + 31 * .12 which becomes 18.31 = 18.31 which is true.\r<BR>\n" );
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document.write( "25.03 = f + 87 * i becomes 25.03 = 14.59 + 87 * .12 which becomes 25.03 = 25.03 which is also true.\r<BR>\n" );
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document.write( "the solution is confirmed to be good.\r<BR>\n" );
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document.write( "the solution is that the fixed cost per month is 14.59 and the incremental cost per minute of calls per month is .12.\r<BR>\n" );
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document.write( "using this solution, the answer to the problem is that the monthly cost for 86 minutes of calls is 14.59 + 86 * .12 = 24.91.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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