document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199003>Question 1199003</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ben's monthly phone bill includes a fixed charge, which is the same each month, and an additional flat rate charge for each long distance call. One month the bill was $32, which included charges for 4 long distance calls. The following month the bill was $38, which included charges for 6 long distance calls. Find the fixed charge and the additional flat-rate charge per long distance call. Assign variables and write the equations <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 #832689 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Ben's monthly phone bill includes a fixed charge, which is the same each month, <BR>\n" );
document.write( "and an additional flat rate charge for each long distance call. <BR>\n" );
document.write( "One month the bill was $32, which included charges for 4 long distance calls. <BR>\n" );
document.write( "The following month the bill was $38, which included charges for 6 long distance calls. <BR>\n" );
document.write( "Find the fixed charge and the additional flat-rate charge per long distance call. <BR>\n" );
document.write( "Assign variables and write the equations<BR>\n" );
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document.write( "<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part 1</H3>\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "First, everything can be solved without any equations.\r\n" );
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document.write( "The difference between the two monthly bills is 38-32 = 6 dollars and 6-4 = 2 calls.\r\n" );
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document.write( "Hense, each call cocts 6/2 = 3 dollars.\r\n" );
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document.write( "Then the fixed monthly charge is  32 - 4*3 = 20 dollars (using the data of the 1st month).\r\n" );
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document.write( "So, the problem is just solved in this way.\r\n" );
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document.write( "<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part 2</H3>\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "With equations, let \"a\" be the fixed monthly charge and let \"b\" is the rate per one call.\r\n" );
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document.write( "Then the monthly cost equation is \r\n" );
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document.write( "    C = a + bx.\r\n" );
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document.write( "where x is the number of calls.\r\n" );
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document.write( "You write it for two consecutive months\r\n" );
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document.write( "    a + 4b = 32,    (1)\r\n" );
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document.write( "    a + 6b = 38.    (2)\r\n" );
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document.write( "Then you subtract equation (1) from equation (2)\r\n" );
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document.write( "        6b - 4b = 38 - 32\r\n" );
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document.write( "           2b   =    6\r\n" );
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document.write( "            b   =    6/2 = 3.    Thus, in this part, you simply REPEAT\r\n" );
document.write( "                                 operations, which I did mentally in the first part.\r\n" );
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document.write( "Having  b= 3,  you find \"a\" from equation (1) as\r\n" );
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document.write( "    a = 32 - 4*3 = 20.           Exactly as I did it in my first solution.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved, with full explanations.\r<BR>\n" );
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document.write( "The lesson to learn from this my lecture is that this problem can be solved mentally<BR>\n" );
document.write( "in couple of seconds without using any equations.\r<BR>\n" );
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document.write( "---------------\r<BR>\n" );
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document.write( "To see many other solved similar and different problems, &nbsp;look into the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/equations/HOW-TO-solve-these-simple-word-problems-MENTALLY-without-using-equations.lesson>HOW TO solve these simple word problems MENTALLY without using equations</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Read it and get be trained in &nbsp;MENTAL &nbsp;solution of similar problems.\r<BR>\n" );
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