document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026655>Question 1026655</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When the original price of an item is increased by a certain rate, the increased price is P3100. When the original price is decreased by the same rate, the decreased priced is P 1900. What is the original price of the item? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641926 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641926\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let p = original price of the item, and r = rate of increase/decrease.\r<BR>\n" );
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document.write( "==> P(1+r) = 3100 and P(1-r) = 1900, as per given information.\r<BR>\n" );
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document.write( "Divide the first equation by the second equation (divide corresponding sides.)\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Br%29%2F%281-r%29+=+31%2F19 ALIGN=MIDDLE  ALT=\"%281%2Br%29%2F%281-r%29+=+31%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19+%2B+19r+=+31+-+31r ALIGN=MIDDLE  ALT=\"19+%2B+19r+=+31+-+31r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50r+=+12 ALIGN=MIDDLE  ALT=\"50r+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> r = 0.24\r<BR>\n" );
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document.write( "==> P(1.24) = 3100 ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+3100%2F1.24+=+2500 ALIGN=MIDDLE  ALT=\"P+=+3100%2F1.24+=+2500\"   DISABLED_style= \"max-width:90%; height:auto;\" > after substituting into the first equation.\r<BR>\n" );
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document.write( "Therefore, P = P2,500, the original price of the item.<BR>\n" );
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