document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072149>Question 1072149</A>: <I><SPAN STYLE=\"word-break: break-all;\">  the price of an item was increased by 10%. this reduced the monthly sales by 20%. find the overall effect on the value of monthly sale </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687041 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=687041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> price was raised by 10%.\r<BR>\n" );
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document.write( "monthly sales were reduced by 20%.\r<BR>\n" );
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document.write( "let x = the original price of each item.<BR>\n" );
document.write( "let y = the original number of units sold.\r<BR>\n" );
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document.write( "the value of the original sales is equal to x * y\r<BR>\n" );
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document.write( "the price is raised 10% to become x + .10 * x = 1.1 * x.\r<BR>\n" );
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document.write( "the number of units sold is decreased by 20% to become y - .20 * y = .8 * y\r<BR>\n" );
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document.write( "the total revenue now becomes 1.1 * x * .8 * y.\r<BR>\n" );
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document.write( "simplify to get total revenue now becomes .88 * x * y\r<BR>\n" );
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document.write( ".88 * x * y / (x * y) = .88 = 88%.\r<BR>\n" );
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document.write( "the effect on the value of the monthly sales is that they are now equal to 88% of what they once were.\r<BR>\n" );
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document.write( "that's a reduction in the value of the monthly sales of 12%.\r<BR>\n" );
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document.write( "this is easier to see with numbers.\r<BR>\n" );
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document.write( "assume the price was 100 dollars per unit and that you sold 100 units each month.\r<BR>\n" );
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document.write( "the value of the monthly sales would be 100 * 100 = $10,000 monthly.\r<BR>\n" );
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document.write( "the price goes up 10% to become $110 per item.\r<BR>\n" );
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document.write( "the monthly units sold goes down 20% to become 80.\r<BR>\n" );
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document.write( "the monthly revenue is now 110 * 80 = $8,800 monthly.\r<BR>\n" );
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document.write( "the difference is $10,000 - $8,800 = $1,200.\r<BR>\n" );
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document.write( "the percent drop in income is $1,200 / $10,000 = .12 = 12%.\r<BR>\n" );
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document.write( "the value of the new monthly sales divided by the value of the old monthly sales is 8,800 / 10,000 = .88 = 88%.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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