document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=220153>Question 220153</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Where N is the size of the file in bytes and t is the number of seconds since the download began. in how many minutes will 25 percent of a 500000-byte file remain to be downloaded round to the nearest minute.\r<BR>\n" );
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document.write( "Percent remaining= 100 - (42000 divided by N)t </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #165354 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=165354\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The statement of your problem has a flaw, or I may be mis-reading it.<BR>\n" );
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document.write( "the formula states:<BR>\n" );
document.write( "Percent remaining = 100 - (42000 divided by N)*T<BR>\n" );
document.write( "It should state:<BR>\n" );
document.write( "Percent Remaining = 100 Percent - (42000 divided by N) * T<BR>\n" );
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document.write( "It would then state as follows:<BR>\n" );
document.write( "Let R = Percent Remaining<BR>\n" );
document.write( "Let N = Number of bytes in the original file.<BR>\n" );
document.write( "Let T = Time in Seconds<BR>\n" );
document.write( "Let X = Transmission Rate per Second.<BR>\n" );
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document.write( "Your formula would then be:<BR>\n" );
document.write( "R = 100% - (X/N)*T<BR>\n" );
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document.write( "R would equal 25%<BR>\n" );
document.write( "X would equal 42000 bytes per second<BR>\n" );
document.write( "N would equal 5000000 bytes<BR>\n" );
document.write( "T is what we would want to solve for.<BR>\n" );
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document.write( "Your formula would become:<BR>\n" );
document.write( "25% = 100% - (42000/5000000)*T<BR>\n" );
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document.write( "We would subtract 25% from both sides of this equation and we would add (42000/5000000)*T to both sides of this equation to get:<BR>\n" );
document.write( "(42000/5000000)*T = 100% - 25% which would become:<BR>\n" );
document.write( ".0084*T = 75%<BR>\n" );
document.write( "We would then divide each side of the equation by .042 to get:<BR>\n" );
document.write( "T = 75%/.0084 = 8928.571429% seconds<BR>\n" );
document.write( "In order to get seconds, we would then have to divide by 100% to get:<BR>\n" );
document.write( "T = 89.28571429 seconds.<BR>\n" );
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document.write( "This is cumbersome and you have to know that you need to divide % seconds by 100% in order to get seconds at the end.<BR>\n" );
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document.write( "The formula would have been much better stated as:<BR>\n" );
document.write( ".25 = 1 - (42000/5000000)*T<BR>\n" );
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document.write( "Then that conversion at the end would not have been necessary.<BR>\n" );
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document.write( "Your general formula would then have been:<BR>\n" );
document.write( "R = 1 - (X/N)*T<BR>\n" );
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document.write( "R would equal Percent Remaining / 100% = 25% / 100% which would equal .25<BR>\n" );
document.write( "X would equal 42000 bytes per second<BR>\n" );
document.write( "N would equal 5000000 bytes<BR>\n" );
document.write( "T is what we would want to solve for and would still be in seconds.<BR>\n" );
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document.write( "Your Formula would become:<BR>\n" );
document.write( ".25 = 1 - (42000/5000000) * T<BR>\n" );
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document.write( "we would solve for T as before.<BR>\n" );
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document.write( "T is stated in seconds.<BR>\n" );
document.write( "The problem requested minutes.<BR>\n" );
document.write( "Divide seconds by 60 seconds per minute to get minutes and your answer becomes:<BR>\n" );
document.write( "T =  89.28571429/ 60 = 1.488095238 minutes<BR>\n" );
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document.write( "To confirm your answer is correct, you would replace your original equation with known values of T and solve to see if it is true.<BR>\n" );
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document.write( "Your original equation is (after my restatement):<BR>\n" );
document.write( "25% = 100% - (42000/5000000)*T<BR>\n" );
document.write( "We would replace T with 1.488095238 * 60 = 89.28571429<BR>\n" );
document.write( "Formula would become:<BR>\n" );
document.write( "25% = 100% - (42000/5000000)*89.28571429 which would become:<BR>\n" );
document.write( "25% = 100% - .75 which would become:<BR>\n" );
document.write( "25% = 100% - 75% after we converted .75 to 75% and would finally become:<BR>\n" );
document.write( "25% = 25% confirming the number of seconds for T was correct.<BR>\n" );
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document.write( "Again, however, we had the complication of % in the equation which would have been eliminated had we converted Percent to Rate up front.<BR>\n" );
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document.write( "Your original equation would then have become:<BR>\n" );
document.write( ".25 = 1 - (42000/5000000)*89.28571429<BR>\n" );
document.write( "which would then have become:<BR>\n" );
document.write( ".25 = 1 - .75 which would then have become:<BR>\n" );
document.write( ".25 = .25 directly without any conversion being necessary.<BR>\n" );
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document.write( "I haven't seen Percents in equations for some time now.  Most of the time they are converted to rates before the equation is solved.  This threw me for a little while but I was finally able to figure it out.  Hopefully this analysis will help you to understand better as well.<BR>\n" );
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