document.write( "Question 1172719: I need help please, here is the problem:\r
\n" ); document.write( "\n" ); document.write( "The costs $C of making a school bag is partly constant and partly varies inversely as the total number N of bags made. When 200 bags are made, the cost per bag is $60. When 500 bags are made, the cost per bag is
\n" ); document.write( "$45. How many bags are made if the cost per bag is $40? Find the cost per bag if 400 bags are made. \n" ); document.write( "

Algebra.Com's Answer #797859 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "The costs $C of making a school bag is partly constant and partly varies inversely as the total number N of bags made.
\n" ); document.write( "When 200 bags are made, the cost per bag is $60. When 500 bags are made, the cost per bag is $45.
\n" ); document.write( "How many bags are made if the cost per bag is $40? Find the cost per bag if 400 bags are made.
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\n" ); document.write( "\n" ); document.write( "The problem's formulation is TERRIBLE (!)\r
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\n" ); document.write( "\n" ); document.write( "This language was in use at parish country schools of the before-Shakespearean times\r
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\n" ); document.write( "\n" ); document.write( "The meaning of this post (if translate it to the contemporary English) is THIS : \r
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document.write( "        Consider the function C(N) = A + (B/N),  where \"A\" and \"B\" are constants, whose values are not known now.\r\n" );
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document.write( "        Given :  C(200) = 60 dollars,   C(500) = 45 dollars.\r\n" );
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document.write( "        Find  N,  if  C(N) = 40 dollars.\r\n" );
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\n" ); document.write( "\n" ); document.write( "OK, now I will start based on my re-formulation.\r
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document.write( "At  N = 200,  we have this equation   \r\n" );
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document.write( "     = 60  dollars     (1)\r\n" );
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document.write( "At  N = 500, we have this equation\r\n" );
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document.write( "     = 45  dollars     (2)\r\n" );
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document.write( "Subtracting equation (2) from equation (1), you get\r\n" );
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document.write( "            -  = 60-45 = 15\r\n" );
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document.write( "Multiply both sides by 1000.  You will get\r\n" );
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document.write( "           5B - 2B = 15000,\r\n" );
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document.write( "             3B    = 15000\r\n" );
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document.write( "              B    = 15000/3 = 5000.\r\n" );
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document.write( "Then from (2)\r\n" );
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document.write( "     = 45,   or\r\n" );
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document.write( "       A + 10 = 45\r\n" );
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document.write( "       A      = 45 - 10 = 35.\r\n" );
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document.write( "To complete the solution, you need find N from the equation\r\n" );
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document.write( "     C(N) = 40,   or   = 40.\r\n" );
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document.write( "The last equation gives\r\n" );
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document.write( "     = 40-35 = 5\r\n" );
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document.write( "        N  =  = 1000.\r\n" );
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document.write( "ANSWER.  N = 1000.\r\n" );
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