document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134655>Question 1134655</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State whether the following statement is true or​ false, and explain why. If the statement is​ false, state the true change.<BR>\n" );
document.write( "If the profits in your consulting business increase by 77​% one year and decrease by 22​% the following​ year, your profits are up by 55​% over two years </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752111 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=752111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> profits increase by 77% one year and decrease by 22% the following year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let's say your profits starts off as x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if they increase by 77%, then the profits for the next year are equal to x + .77 * x which makes them equal to 1.77 * x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if they then decrease by 22% the following year, then the profits for the following year would be 1.77 * x - .22 * 1.77 * x = 1.3806 * x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your profits went from x to 1.3806 * x over the two year period.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's an increase of .3806 * x which is equal to 38.06%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's how i think it works in dollars and cents.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assume your profits are 72 dollars for this year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the next year they are increased by 77%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the increase is therefore .77 * 72 = 55.44.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the profits next year are 72 + 55.44 = 127.44.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your profits the year after are decreased by 22%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "127.44 - .22 * 127.44 = 99.4032.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your profits over the two years are 99.4032 minus 72 = 27.4032.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that increase is 27.4032 / 72 = .3806 * 100 = 38.06%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the 22% was taken off of next year's profit, not this year's profit.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );