document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209265>Question 1209265</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In one month a store sold pads of paper, some for $14, some for $5 and some for 50¢. A total of 54 pads were sold for a total of $54. Evaluate the total number of the 50¢ pads sold minus the number of $5 pads sold.<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 #847938 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There's probably a much more efficient way to do this, but here's my approach.\r<BR>\n" );
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document.write( "x = number of $14 pads<BR>\n" );
document.write( "y = number of $5 pads<BR>\n" );
document.write( "z = number of 50 cent pads<BR>\n" );
document.write( "The goal is to evaluate z-y\r<BR>\n" );
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document.write( "54 pads were sold<BR>\n" );
document.write( "x+y+z = 54<BR>\n" );
document.write( "which can be rearranged to<BR>\n" );
document.write( "z = 54-x-y\r<BR>\n" );
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document.write( "14x = money from just the $14 pads<BR>\n" );
document.write( "5y = money from just the $5 pads<BR>\n" );
document.write( "0.5z = money from just the 50 cent pads<BR>\n" );
document.write( "These must total to the $54 mentioned.\r<BR>\n" );
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document.write( "14x+5y+0.5z = 54<BR>\n" );
document.write( "14x+5y+0.5*(54-x-y) = 54<BR>\n" );
document.write( "14x+5y+27-0.5x-0.5y = 54<BR>\n" );
document.write( "13.5x+4.5y+27 = 54<BR>\n" );
document.write( "13.5x+4.5y = 54-27<BR>\n" );
document.write( "13.5x+4.5y = 27<BR>\n" );
document.write( "135x+45y = 270<BR>\n" );
document.write( "45y = -135x+270<BR>\n" );
document.write( "y = (-135x+270)/45<BR>\n" );
document.write( "y = (-135x)/45+270/45<BR>\n" );
document.write( "y = -3x+6\r<BR>\n" );
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document.write( "If x and y are positive integers, then the only possibility is when x = 1<BR>\n" );
document.write( "If x = 2 or larger, then y = 0 or smaller.<BR>\n" );
document.write( "I'll assume that at least one of each item was sold.\r<BR>\n" );
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document.write( "If x = 1 then y = -3x+6 = -3*1+6 = 3<BR>\n" );
document.write( "and z = 54-x-y = 54-1-3 = 50\r<BR>\n" );
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document.write( "x = 1 copy of the $14 pad of paper was sold<BR>\n" );
document.write( "y = 3 copies of the $5 pad of paper were sold<BR>\n" );
document.write( "z = 50 copies of the 50 cent pad of paper were sold\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "x+y+z = 1+3+50 = 54<BR>\n" );
document.write( "and<BR>\n" );
document.write( "14x+5y+0.50z = 14*1+5*3+0.50*50 = 54<BR>\n" );
document.write( "Both conditions are confirmed.\r<BR>\n" );
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document.write( "The final answer is therefore z-y = 50-3 = <font color=red>47</font><BR>\n" );
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