document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75007>Question 75007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A writing workshop enrolls novelists and poets in a ratio of 5 to 3. There are 24 people at the workshop. How many novelists are there? How many poets are poets are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53920 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=53920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at it this way ... for every 8 people, 5 are novelists. Therefore, you can write the<BR>\n" );
document.write( "proportion:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F8+=+x%2F24 ALIGN=MIDDLE  ALT=\"5%2F8+=+x%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can read this as, \"5 out of every 8 is the same as x out of 24.\"  x will be the number<BR>\n" );
document.write( "of novelists enrolled in a group of 24 people.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "In proportions such as this you can solve for the unknown by first cross multiplying.<BR>\n" );
document.write( "This means multiply the numerator of the first fraction by the denominator of the second fraction.<BR>\n" );
document.write( "Then multiply the denominator of the first fraction times the numerator of the second fraction.<BR>\n" );
document.write( "Then set the two products equal and solve for x.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This translates to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A24=+8%2Ax ALIGN=MIDDLE  ALT=\"5%2A24=+8%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply out the left side to get 120. This makes the problem:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120+=+8%2Ax ALIGN=MIDDLE  ALT=\"120+=+8%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Divide both sides by 8 and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2F8+=+x ALIGN=MIDDLE  ALT=\"120%2F8+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So, in a group of 24 persons, 15 will be novelists.  That means the remaining 9 persons must<BR>\n" );
document.write( "be poets.  So, we can now check the ratio of novelists to poets and see if it is 5 to 3 as<BR>\n" );
document.write( "stated in the problem.  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F9+=+5%2A3%2F%283%2A3%29+=+5%2Across%283%29%2F%283%2Across%283%29%29+=+5%2F3 ALIGN=MIDDLE  ALT=\"15%2F9+=+5%2A3%2F%283%2A3%29+=+5%2Across%283%29%2F%283%2Across%283%29%29+=+5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The answer checks.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand proportions.  And don't forget that you can solve proportions<BR>\n" );
document.write( "by cross multiplying.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );