document.write( "Question 1201604: A shopkeeper bought x chairs for a total cost of $650. He sold them at $4 each more than they had cost him . Six chairs were damaged and could not be sold . If he made a profit of $98 on the whole transaction , form and solve an equation in x . \r
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\n" ); document.write( "\n" ); document.write( "x(x-6)-650=98
\n" ); document.write( "x^2-6x-748=0 (can't be factored)
\n" ); document.write( "The answer on my book is 50 .
\n" ); document.write( "So, how is this solved? \n" ); document.write( "

Algebra.Com's Answer #836063 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A shopkeeper bought x chairs for a total cost of $650.
\n" ); document.write( "He sold them at $4 each more than they had cost him.
\n" ); document.write( "Six chairs were damaged and could not be sold .
\n" ); document.write( "If he made a profit of $98 on the whole transaction, form and solve an equation in x.
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document.write( "The price he bought them was    dollars per chair.\r\n" );
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document.write( "He made a profit of $98 on the whole transaction - hence, he sold (x-6) chairs for 650+98 = 748 dollars.\r\n" );
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document.write( "Thus the price he sold the chairs was    dollars per chair.\r\n" );
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document.write( "The difference between the selling price and buying price was $4 (given) - so we write this equation\r\n" );
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document.write( "     -  = 4  dollars.\r\n" );
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document.write( "    +---------------------------------------------+\r\n" );
document.write( "    |   At this point, the setup is complete.     |\r\n" );
document.write( "    |   Now your task is to solve this equation.  |\r\n" );
document.write( "    +---------------------------------------------+\r\n" );
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document.write( "For it, multiply both sides by x*(x-6).  You will get\r\n" );
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document.write( "    748x - 650(x-6) = 4x*(x-6).\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "    748x - 650x + 650*6 = 4x^2 - 24x\r\n" );
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document.write( "    98x + 3900 = 4x^2 - 24x\r\n" );
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document.write( "    4x^2 - 24x - 98x - 3900 = 0\r\n" );
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document.write( "    4x^2 - 122x - 3900 = 0\r\n" );
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document.write( "    2x^2 - 61x - 1950 = 0.\r\n" );
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document.write( "Apply the quadratic formula.\r\n" );
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document.write( "You will get two roots: one positive and one negative.\r\n" );
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document.write( "The positive root is 50.\r\n" );
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document.write( "Discard the negative root and accept the positive one.\r\n" );
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document.write( "ANSWER.  x = 50 chairs were bought.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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