document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=626893>Question 626893</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 2005, there were 11,500 students at college A, with a projected enrollment increase of 1,200 students per year. In the same year, there were 22,700 students at college B, with a projected enrollment decline of 400 students per year. in what year will the two colleges have the same enrollment? At that time how many students be enrolled in both colleges?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #394485 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=394485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In 2005, there were 11,500 students at college A, with a projected enrollment increase of 1,200 students per year. In the same year, there were 22,700 students at college B, with a projected enrollment decline of 400 students per year. in what year will the two colleges have the same enrollment? At that time how many students be enrolled in both colleges?<BR>\n" );
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document.write( "We have two straight line equations that take the standard form: y=mx+b, m=slope, b=y-intercept.<BR>\n" );
document.write( "For given problem, college A:<BR>\n" );
document.write( "y-intercept, b=11500<BR>\n" );
document.write( "slope, m=1200 students per year increase<BR>\n" );
document.write( "equation: y=1200x+11500 (number of students for given year x)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given problem, college B:<BR>\n" );
document.write( "y-intercept, b=22700<BR>\n" );
document.write( "slope, m=-400 students per year decrease<BR>\n" );
document.write( "equation: y=-400x+22700 (number of students for given year x)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "When number of students are the same for both colleges:<BR>\n" );
document.write( "1200x+11500=-400x+22700<BR>\n" );
document.write( "1600x=11200<BR>\n" );
document.write( "x=11200/1600<BR>\n" );
document.write( "x=7<BR>\n" );
document.write( "y=1200x+11500=19900.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "The two colleges will have the same enrollment in year 2012<BR>\n" );
document.write( "Number of students enrolled at both colleges at this time: 19,900\r<BR>\n" );
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document.write( "note: It would be instructive to plot both equations on an x-y coordinate system and see that the answer is the point of intersection of these two equations.\r<BR>\n" );
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