document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105453>Question 1105453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A woman bought a number of items for $36. She realized that if she had bought 6 more items for the same money, she would have paid $3 less per item. How many items did she buy?\r<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 #720278 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x is the number of items bought.<BR>\n" );
document.write( "y is the price per item.\r<BR>\n" );
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document.write( "x * y = 36\r<BR>\n" );
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document.write( "if she bought 6 more items, she would have paid 3 dollars less per item and the total cost would still have been 36 dollars.\r<BR>\n" );
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document.write( "(x+6) * (y-3) = 36\r<BR>\n" );
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document.write( "from the first equation, solve for y to get y = 36/x.\r<BR>\n" );
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document.write( "in the second equation, replace y with 36/x to get (x + 6) * (36/x - 3) = 36\r<BR>\n" );
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document.write( "multiply both sides of the equation by x to get x * (x + 6) * (36/x - 3) = 36 * x\r<BR>\n" );
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document.write( "simplify to get (x^2 + 6x) * (36/x - 3) = 36x.\r<BR>\n" );
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document.write( "distribute the multiplication to get 36x - 3x^2 + 216 - 18x = 36x.\r<BR>\n" );
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document.write( "the 36x on both sides of the equation cancels out and you are left with -3x^2 + 216 - 18x = 0\r<BR>\n" );
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document.write( "reorder the terms in descending order of degree to get -3x^2 - 18x + 216 = 0\r<BR>\n" );
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document.write( "factor this equation to get x = 6 or x = -12.\r<BR>\n" );
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document.write( "x can't be negative, so x = 6.\r<BR>\n" );
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document.write( "i the equation of xy = 36, replace x with 6 to get 6y = 36.\r<BR>\n" );
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document.write( "solve for y to get y = 6.\r<BR>\n" );
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document.write( "x is the number of items bought.<BR>\n" );
document.write( "y is the price per item.\r<BR>\n" );
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document.write( "she bought 6 items at 6 dollars each for a total of 36 dollars.\r<BR>\n" );
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document.write( "if she bought 6 more items, then the price per item would have been 3 dollars less.\r<BR>\n" );
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document.write( "(x+6) * (y-3) = 36\r<BR>\n" );
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document.write( "x = 6 and y = 6, therefore (6+6) * (6-3) = 36 which becomes 12 * 3 = 36 which is true.\r<BR>\n" );
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document.write( "everything checks out so your solution is that she bought 6 items.\r<BR>\n" );
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