document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=817273>Question 817273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number of freshman tried out for the track team.\r<BR>\n" );
document.write( "\n" );
document.write( "after the first round of tryouts, 1/2 of the freshmen were cut.<BR>\n" );
document.write( "after the second round, 1/3 of the freshmen were cut.<BR>\n" );
document.write( "after the third round, 1/4 of the freshmen were cut.<BR>\n" );
document.write( "after the fourth round 1/5 of the freshmen were cut.<BR>\n" );
document.write( "after the fifth round, 1/6 of the freshmen were cut.\r<BR>\n" );
document.write( "\n" );
document.write( "There were 10 freshmen left who made the team. How many tried out initially? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491974 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3759)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=491974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The key to this problem is to focus on the fraction of freshmen who were not cut, not on the fraction that were cut.<br><BR>\n" );
document.write( "Let x = the initial number of freshmen who tried out.<BR>\n" );
document.write( "After the first round 1/2 were cut. If 1/2 were cut then 1/2 were not cut. So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x ALIGN=MIDDLE  ALT=\"%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "would be the number who were not cut during the first round. In the next round 1/3 were cut. So 2/3 were not cut making:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%281%2F2%29x ALIGN=MIDDLE  ALT=\"%282%2F3%29%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the number of freshmen not cut after two rounds. Next 1/4 were cut and 3/4 were not. So:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29%282%2F3%29%281%2F2%29x ALIGN=MIDDLE  ALT=\"%283%2F4%29%282%2F3%29%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "were still in it after 3 rounds. Then 1/5 were cut and 4/5 were not making<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F5%29%283%2F4%29%282%2F3%29%281%2F2%29x ALIGN=MIDDLE  ALT=\"%284%2F5%29%283%2F4%29%282%2F3%29%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the number of freshmen who were not cut after 4 rounds. Next 1/6 were cut and 5/6 were not. So:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F6%29%284%2F5%29%283%2F4%29%282%2F3%29%281%2F2%29x ALIGN=MIDDLE  ALT=\"%285%2F6%29%284%2F5%29%283%2F4%29%282%2F3%29%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "After all this there were 10 left. So:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F6%29%284%2F5%29%283%2F4%29%282%2F3%29%281%2F2%29x+=+10 ALIGN=MIDDLE  ALT=\"%285%2F6%29%284%2F5%29%283%2F4%29%282%2F3%29%281%2F2%29x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we solve for x. A lot of canceling can be done on the left side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%285%29%2F6%29%28cross%284%29%2Fcross%285%29%29%28cross%283%29%2Fcross%284%29%29%28cross%282%29%2Fcross%283%29%29%281%2Fcross%282%29%29x+=+10 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "leaving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29%281%2F1%29%281%2F1%29%281%2F1%29%281%2F1%29x+=+10 ALIGN=MIDDLE  ALT=\"%281%2F6%29%281%2F1%29%281%2F1%29%281%2F1%29%281%2F1%29x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29x+=+10 ALIGN=MIDDLE  ALT=\"%281%2F6%29x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying by 6:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+60 ALIGN=MIDDLE  ALT=\"x+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "60<BR>\n" );
document.write( "Keep 1/2 => 30<BR>\n" );
document.write( "Keep 2/3 => 20<BR>\n" );
document.write( "Keep 3/4 => 15<BR>\n" );
document.write( "Keep 4/5 => 12<BR>\n" );
document.write( "Keep 5/6 => 10 Check! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );