document.write( "Question 1195152: The Phone-A-Way company offers two different monthly cell phone plus. Plan X costs $0.25 for each minute of talk-time. Plan Y costs $9.75 for up to 150 minutes of talk-time and $0.50 for each additional minute. If the two plans cost the same for a month in which m minutes of talk-time are used, where m>40 what is the value of m? \n" ); document.write( "

Algebra.Com's Answer #827542 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "The Phone-A-Way company offers two different monthly cell phone plus.
\n" ); document.write( "Plan X costs $0.25 for each minute of talk-time.
\n" ); document.write( "Plan Y costs $9.75 for up to 150 minutes of talk-time and $0.50 for each additional minute.
\n" ); document.write( "If the two plans cost the same for a month in which m minutes of talk-time are used,
\n" ); document.write( "where m > 40 what is the value of m?
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document.write( "Consider coordinate plane (minutes, dollars), where minutes are horizontal coordinate axis;\r\n" );
document.write( "vertical coordinate line is for dollars.\r\n" );
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document.write( "Plan X graphically is the sloped straight line through the origin of the coordinate system\r\n" );
document.write( "(minutes,dollars) with the slope of 0.25 dollars per minute.\r\n" );
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document.write( "Plan Y is the horizontal line Y = 9.75 from  m= 0 minute  to m= 150 minutes inclusive;\r\n" );
document.write( "then after m > 150 minutes it is the straight line with the slope 0.5 dollars per minute.\r\n" );
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document.write( "    +--------------------------------------------------------+\r\n" );
document.write( "    |    Make a sketch in accordance with this description.  |\r\n" );
document.write( "    |    From the sketch, notice that line X                 |\r\n" );
document.write( "    |    intersects line Y at two pints.                     |\r\n" );
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document.write( "First intersection point is when  0.25m = 9.75 dollars;  it is at  m =  = 39 minutes.\r\n" );
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document.write( "Since we consider m > 40 (see the condition), this intersection point is out of our interest.\r\n" );
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document.write( "Next intersection point is when  0.25m = 9.75 + 0.5*(m-150).\r\n" );
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document.write( "Find m from this equation, simplifying it step by step\r\n" );
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document.write( "    0.25m = 9.75 + 0.5m - 0.5*150\r\n" );
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document.write( "    0.25m - 0.5m = 9.75 - 0.5*150\r\n" );
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document.write( "        - 0.25m  =    -65.25\r\n" );
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document.write( "              m  =     = 261 minutes.\r\n" );
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document.write( "It is your ANSWER: the value of m satisfying to imposed conditions is 261 minutes.\r\n" );
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document.write( "CHECK.  At m= 261, plan X costs  261*0.25 = 65.25 dollars.\r\n" );
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document.write( "        At t = 261, plan Y costs 9.75 + 0.5*(261-150) = 65.25 dollars, i.e. the same amount,\r\n" );
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document.write( "                    which shows that the solution and the answer are correct.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, checked and fully explained.\r
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\n" ); document.write( "\n" ); document.write( "In this problem, the mathematical model is the system of two equations,
\n" ); document.write( "one is linear and the other is non-linear. The whole system is non-linear.\r
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\n" ); document.write( "\n" ); document.write( "From my post, learn on how to solve such non-linear system of two equations.\r
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