document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=587964>Question 587964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!!<BR>\n" );
document.write( "Due to inflation the price of an item was increased twice, after the second increase the price became 6 times the original. By what percent was the second increase if the first increase was 50%? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #374336 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=374336\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> LOT OF EXPLANATIONS (optional reading):<BR>\n" );
document.write( "When you increase the price by 50%, you add to the previous price 50% of the previous price. That is 0.50 or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2F100 ALIGN=MIDDLE  ALT=\"50%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the previous price.<BR>\n" );
document.write( "So, if you started with a price P, after a 50% increase, the new price is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2B%2850%2F100%29%2AP ALIGN=MIDDLE  ALT=\"P%2B%2850%2F100%29%2AP\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2B0.5P=P%281%2B0.5%29=1.5P ALIGN=MIDDLE  ALT=\"P%2B0.5P=P%281%2B0.5%29=1.5P\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The idea, to calculate the new price after a certain percent increase or decrease is:<BR>\n" );
document.write( "1) express that percent as a decimal (0.5 for 50%, 0.27 for 27%, 0.045 for 4.5%, and so on), using negative numbers for price decreases.<BR>\n" );
document.write( "2) add 1 to that, to get your increase factor<BR>\n" );
document.write( "3) multiply the old price times that factor<BR>\n" );
document.write( "Example, a $60 dress, on sale at 12% off, costs<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2A%281-0.12%29 ALIGN=MIDDLE  ALT=\"60%2A%281-0.12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2A0.88 ALIGN=MIDDLE  ALT=\"60%2A0.88\"   DISABLED_style= \"max-width:90%; height:auto;\" >=$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52.80 ALIGN=MIDDLE  ALT=\"52.80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "THE SOLUTION:<BR>\n" );
document.write( "From an original price, P, an increase of 50% (0.5 as a decimal) brings the price up to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2B0.5P=P%281%2B0.5%29=1.5P ALIGN=MIDDLE  ALT=\"P%2B0.5P=P%281%2B0.5%29=1.5P\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "A new increase of x (expressed as a decimal) brings the price up to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5P%281%2Bx%29 ALIGN=MIDDLE  ALT=\"1.5P%281%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If that equals 6 times the original price,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5P%281%2Bx%29=6P ALIGN=MIDDLE  ALT=\"1.5P%281%2Bx%29=6P\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We divide both sides by P, eliminating P, and then solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5P%281%2Bx%29=6P ALIGN=MIDDLE  ALT=\"1.5P%281%2Bx%29=6P\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%281%2Bx%29=6 ALIGN=MIDDLE  ALT=\"1.5%281%2Bx%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2B1.5x=6 ALIGN=MIDDLE  ALT=\"1.5%2B1.5x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2B1.5x-1.5=6-1.5 ALIGN=MIDDLE  ALT=\"1.5%2B1.5x-1.5=6-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5x=4.5 ALIGN=MIDDLE  ALT=\"1.5x=4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5x%2F1.5=4.5%2F1.5 ALIGN=MIDDLE  ALT=\"1.5x%2F1.5=4.5%2F1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A decimal of 3.00 mean an increase of 300%.<BR>\n" );
document.write( " <BR>\n" );
document.write( "COMMENTS (more optional reading):<BR>\n" );
document.write( "That is quite an increase.<BR>\n" );
document.write( "If the original price was $200, the first 50% increase would have brought the price to $300.<BR>\n" );
document.write( "Then the second (300%) increase would have quadrupled the previous $300 price to $1200, 6 times the original price.<BR>\n" );
document.write( "That's hyperinflation. Ask anyone from Buenos Aires about it.<BR>\n" );
document.write( "(There are other places that have had bad hyperinflation, but none that I visited). </SPAN>\n" );
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