document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356190>Question 356190</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the north campus of a small liberal arts college, 10% of the students are women.  At the south campus, 50% of the students are women.  The campuses are merged into one east campus.  If 40% of the 1200 students at the east campus are women, how many students did each of the north and south campuses have before the merger? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254328 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=254328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At the north campus of a small liberal arts college, 10% of the students are women. At the south campus, 50% of the students are women. The campuses are merged into one east campus. If 40% of the 1200 students at the east campus are women, how many students did each of the north and south campuses have before the merger?<BR>\n" );
document.write( "==<BR>\n" );
document.write( "let N=total students at North campus<BR>\n" );
document.write( "Let S=total students at South campus<BR>\n" );
document.write( "--<BR>\n" );
document.write( "given <BR>\n" );
document.write( "North campus merged with South campus to create east campus of 1200 students<BR>\n" );
document.write( "eq 1, total students: N+S=1200<BR>\n" );
document.write( "eq 2, women:  0.10N+0.50S=0.40*1200=480<BR>\n" );
document.write( "--<BR>\n" );
document.write( "step 1: N+5S=4800   multiply eq 2 by 10<BR>\n" );
document.write( "step 2: N=1200-S    solve for N in eq1<BR>\n" );
document.write( "step 3:  (1200-S)+5S=4800   substitute step 2 into step 1<BR>\n" );
document.write( "step 4: 4S=3600        group similar terms<BR>\n" );
document.write( "step 5: S=900<BR>\n" );
document.write( "step 6:  N=1200-S therefore  N=1200-900=300<BR>\n" );
document.write( "==<BR>\n" );
document.write( "validate<BR>\n" );
document.write( "go to eq1 and eq2 substitute S=900 and N=300 <BR>\n" );
document.write( "N+S=300+900=1200 checked<BR>\n" );
document.write( "0.1N+0.5S=480 ==>   0.1*300+0.5*900=30+450=480  checked<BR>\n" );
document.write( "==<BR>\n" );
document.write( "answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28N=300%29 ALIGN=MIDDLE  ALT=\"highlight_red%28N=300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28S=900%29 ALIGN=MIDDLE  ALT=\"highlight_red%28S=900%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );