document.write( "Question 1125874: A women bought a number of items for $48. She realizes that if she bought 6 more items for the same money, she would have paid $4 less per item. How many items did she buy? \n" ); document.write( "

Algebra.Com's Answer #742242 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The original formulation in the post is TERRIBLE (from the common sense of view).\r
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\n" ); document.write( "\n" ); document.write( "            And it is the main reason why the problem seems to be upside-down, staying on the head.\r
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\n" ); document.write( "\n" ); document.write( "            So the first step is to transform it to the right form.\r
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\n" ); document.write( "\n" ); document.write( "            Much more reasonable (classic form) formulation (after editing) is this:\r
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document.write( "    A women bought a number of equally priced items for $48. Had the price be $4 less for each item,  she could buy 6 more items \r\n" );
document.write( "    for the same money. How many items did she buy?\r\n" );
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\n" ); document.write( "\n" ); document.write( "In this formulation, the standard algebra solution is and works as follows.\r
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document.write( "    x*p = 48,            (1)\r\n" );
document.write( "    (x+6)*(p-4) = 48.    (2)\r\n" );
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document.write( "Simplify equation (2) :\r\n" );
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document.write( "    xp + 6p - 4x - 24 = 48.\r\n" );
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document.write( "Replace the term xp in the left side of the last equation by 48, based on (1) :\r\n" );
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document.write( "    48 + 6p - 4x - 24 = 48,\r\n" );
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document.write( "    6p - 4x = 24.        (3)\r\n" );
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document.write( "From equation (3), express p =   and substitute it into equation (1). You will get\r\n" );
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document.write( "     = 48,\r\n" );
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document.write( "    x*(24+4x) = 288\r\n" );
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document.write( "    4x^2 +24x - 288 = 0\r\n" );
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document.write( "    x^2 + 6x - 72 = 0\r\n" );
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document.write( "    (x+12)*(x-6) = 72.\r\n" );
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document.write( "The positive root (which only makes sense) is 6.\r\n" );
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document.write( "Answer.  The women bought 6 items.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Was it so ugly ?\r
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\n" ); document.write( "\n" ); document.write( "But of course, not - if you know on how to do it in a correct way.
\n" ); document.write( "Simply a standard (and a smooth) algebra solution, and you should learn on how to solve it algebraically -
\n" ); document.write( "simply because you can meet many of such problems in your student years.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Had they sold . . .\r
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