document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199482>Question 1199482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people. Calculate the lower bound for the number of minutes it takes for all the people to leave. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833392 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "p = number of people\r<BR>\n" );
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document.write( "The true value of p is unknown, but we know that it rounds to 29800 when rounding to the nearest hundred people.\r<BR>\n" );
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document.write( "The smallest p could be is 29750 since that rounds to 29800. <BR>\n" );
document.write( "The largest is 29849; note that 29850 rounds to 29900.\r<BR>\n" );
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document.write( "We have this interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29750+%3C=+p+%3C=+29849 ALIGN=MIDDLE  ALT=\"29750+%3C=+p+%3C=+29849\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "r = the rate in which the people leave<BR>\n" );
document.write( "This rate is in \"people per minute\".\r<BR>\n" );
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document.write( "Like p, the true value of r is unknown.<BR>\n" );
document.write( "The midpoint of 350 and 400 is (350+400)/2 = 375, which represents the smallest value r could be if we round to the nearest 50.<BR>\n" );
document.write( "The value 374 would round to 350.\r<BR>\n" );
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document.write( "On the other side of the spectrum, (400+450)/2-1 = 425-1 = 424 rounds to 400 as well when rounding to the nearest 50. <BR>\n" );
document.write( "The value 425 rounds to 450.\r<BR>\n" );
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document.write( "To wrap this section up, you have this interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=375%3C=r%3C=424 ALIGN=MIDDLE  ALT=\"375%3C=r%3C=424\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Summary so far:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29750+%3C=+p+%3C=+29849 ALIGN=MIDDLE  ALT=\"29750+%3C=+p+%3C=+29849\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=375%3C=r%3C=424 ALIGN=MIDDLE  ALT=\"375%3C=r%3C=424\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "where p is the number of people and r is the rate in which they leave (in people per minute).\r<BR>\n" );
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document.write( "If we have the smallest number of people (29750) and the highest rate in which they leave (424), then we'll get the lower bound of how long it takes everyone to leave. <BR>\n" );
document.write( "This can be thought of as the floor value.\r<BR>\n" );
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document.write( "time = (number of people)/(rate)<BR>\n" );
document.write( "time = (29750)/(424)<BR>\n" );
document.write( "time = 70.1650943396227<BR>\n" );
document.write( "time = 70.165\r<BR>\n" );
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document.write( "Answer: Approximately 70.165 minutes.<BR>\n" );
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