document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269002>Question 269002</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would you work out this problem; It requires to show all work!\r<BR>\n" );
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document.write( "The cafeteria has 360 roses to sell for Valentine's Day.  You want to pick<BR>\n" );
document.write( "out a perfect red rose for someone special.  When you get to the cafeteria<BR>\n" );
document.write( "you discover:\r<BR>\n" );
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document.write( "*every third rose is too short<BR>\n" );
document.write( "*every fourth rose has too many thorns<BR>\n" );
document.write( "*every fifth rose is wilted<BR>\n" );
document.write( "*every sixth rose is pink<BR>\n" );
document.write( "*every eighth rose is yellow\r<BR>\n" );
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document.write( "If these are the only problems that the roses have, how many perfect roses are<BR>\n" );
document.write( "there for you to choose from?\r<BR>\n" );
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document.write( "The problem requires to show all work.  I would think that there is an<BR>\n" );
document.write( "algebraic expression that would help me out, but I am in need of help.<BR>\n" );
document.write( "I can help myself by making pictures to help visualize, but I think there must<BR>\n" );
document.write( "be a better way.\r<BR>\n" );
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document.write( "Please help me if you can.   Thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197146 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=197146\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F3+=+120 ALIGN=MIDDLE  ALT=\"360%2F3+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 120 roses that are too short<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F4+=+90 ALIGN=MIDDLE  ALT=\"360%2F4+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 90 roses that have too many thorns<BR>\n" );
document.write( "But, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A4+=+12 ALIGN=MIDDLE  ALT=\"3%2A4+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, every 12th rose was also divisible by 3,<BR>\n" );
document.write( "and was also a too short rose,and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F12+=+30 ALIGN=MIDDLE  ALT=\"360%2F12+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so 30 of the 90 are being counted twice. Just add<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90+-+30+=+60 ALIGN=MIDDLE  ALT=\"90+-+30+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the list of not wanted<BR>\n" );
document.write( "So far I have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120+%2B+60+=+180 ALIGN=MIDDLE  ALT=\"120+%2B+60+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > not wanted<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F5+=+72 ALIGN=MIDDLE  ALT=\"360%2F5+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Of these every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A4%2A5+=+60 ALIGN=MIDDLE  ALT=\"3%2A4%2A5+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > roses is being counted twice<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F60+=+6 ALIGN=MIDDLE  ALT=\"360%2F60+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72+-+6+=+66 ALIGN=MIDDLE  ALT=\"72+-+6+=+66\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "66 roses are wilted and are not being counted twice<BR>\n" );
document.write( "So far I have: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120+%2B+60+%2B+66+=+246 ALIGN=MIDDLE  ALT=\"120+%2B+60+%2B+66+=+246\"   DISABLED_style= \"max-width:90%; height:auto;\" > not wanted<BR>\n" );
document.write( "Every 6th rose is pink, but all these were counted as<BR>\n" );
document.write( "a too short rose, since dividing by 6 is included by<BR>\n" );
document.write( "dividing by 3, therefore don't count these<BR>\n" );
document.write( "Likewise, every 8th rose was also counted when I counted <BR>\n" );
document.write( "every 4th rose that had too many thorns,so don't count<BR>\n" );
document.write( "these<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360+-+246+=+114 ALIGN=MIDDLE  ALT=\"360+-+246+=+114\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "114 roses of the 360 are perfect<BR>\n" );
document.write( "I could have stumbled with my logic, but I<BR>\n" );
document.write( "think this is right- hope yo at least un-<BR>\n" );
document.write( "derstand what I'm doing<BR>\n" );
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