document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211426>Question 211426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Respected sir,\r<BR>\n" );
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document.write( "plz help me to slove this % problem.\r<BR>\n" );
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document.write( "1] At car delarship X,the total profil from sales increased by 10% over the previous year while the number of cars sold decreased by 10% over the previous year.Approximately what was the average percent increase in profit per car over the previous year?\r<BR>\n" );
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document.write( "waiting for yur reply.\r<BR>\n" );
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document.write( "Thanks.<BR>\n" );
document.write( "Regards<BR>\n" );
document.write( "Binita. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159786 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=159786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your problem is:<BR>\n" );
document.write( "1] At car delarship X,the total profit from sales increased by 10% over the previous year while the number of cars sold decreased by 10% over the previous year.<BR>\n" );
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document.write( "Approximately what was the average percent increase in profit per car over the previous year?<BR>\n" );
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document.write( "let P = total profit made the previous year.<BR>\n" );
document.write( "let C = number of cars sold the previous year.<BR>\n" );
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document.write( "Average Profit = Total Profit divided by number of cars sold.<BR>\n" );
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document.write( "let A = average profit per car made the previous year.<BR>\n" );
document.write( "Formula for calculating average profit per car from the previous year becomes:<BR>\n" );
document.write( "A = P/C<BR>\n" );
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document.write( "This year the total profit increased by 10% over the previous year.<BR>\n" );
document.write( "This makes the total profit this year equal to P + .1*P = 1.1 * P<BR>\n" );
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document.write( "This year the number of cars sold decreased by 10% over the previous year.<BR>\n" );
document.write( "This makes the total number of cars sold this year equal to C - .1*C which equals .9 * C<BR>\n" );
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document.write( "let B = average profit per car made this year.<BR>\n" );
document.write( "Formula for calculating average profit per car this year becomes:<BR>\n" );
document.write( "B = 1.1 * P / .9 * C<BR>\n" );
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document.write( "This is the same as:<BR>\n" );
document.write( "B = (1.1/.9) * (P/C)<BR>\n" );
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document.write( "1.1/.9 = 1.22222222...<BR>\n" );
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document.write( "This means that the average profit this year per car increased 22.222222... % over the average profit per car from the previous year.<BR>\n" );
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document.write( "This is how that works.<BR>\n" );
document.write( "A = average profit per car last year = P/C<BR>\n" );
document.write( "B = average profit per car this year = (1.1*P)/(.9*C)<BR>\n" );
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document.write( "(1.1P/.9C)/(P/C) is the same as:<BR>\n" );
document.write( "(1.1P/.9C)*(C/P)<BR>\n" );
document.write( "P/C cancels out C/P so you are left with 1.1/.9.<BR>\n" );
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document.write( "The result is that B/A = 1.1/.9 = 1.22222222... which is the same as an increase of 22.22222... % <BR>\n" );
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document.write( "B/A = 1.1/.9 becomes:<BR>\n" );
document.write( "B = A*1.1/.9 when you solve for B by multiplying both sides of this equation by A.<BR>\n" );
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document.write( "A*1.1/.9 becomes A*1.22222.... when you divide 1.1 by .9.<BR>\n" );
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document.write( "A * 1.22222.... is the same as A + .22222... * A<BR>\n" );
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document.write( ".22222... * A is the same as 22.22222% * A when you multiply .222 * 100% to turn it into a percent rather than a ratio.<BR>\n" );
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document.write( "let me put this into numbers so you can see it better.<BR>\n" );
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document.write( "let C = 1,000<BR>\n" );
document.write( "let P = 5,000,000<BR>\n" );
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document.write( "A = average profit per car = P/C = 5,000,000/1,000 = 5,000 dollars profit per car.<BR>\n" );
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document.write( "This year the total profit went up 10% over last year.<BR>\n" );
document.write( "P + 10% * P = 1.1 * P = 1.1 * 5,000,000 = 5,500,000<BR>\n" );
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document.write( "this year the total number of cars sold went down 10% over last year.<BR>\n" );
document.write( "C - 10% * C = .9 * C = .9 * 1,000 = 900<BR>\n" );
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document.write( "B = average profit per car this year = 1.1*P/.9*C = 5,500,000/900 = 6111.11111... per car.<BR>\n" );
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document.write( "6111.11111... / 5000 = 1.222222222... <BR>\n" );
document.write( "This means that average profit per car this year increased by 22.22...% over last year.<BR>\n" );
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document.write( "Rounding this to the nearest hundredth of a percent makes the answer equal to:<BR>\n" );
document.write( "Average increase in profit per car this year equals 22.22%<BR>\n" );
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document.write( " </SPAN>\n" );
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