document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=25721>Question 25721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On the first day of school, the percentage of boys in a particular class is 60%.  During the school year, six girls move away, and are replaced in the class by six boys; this makes the class roster 75% boys.  Find the number of boys and girls in the class on the first day of school.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13832 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=13832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let b = number of boys on the 1st day of school<BR>\n" );
document.write( "let g = number of girls on the 1st day of school<BR>\n" );
document.write( "so, b + g equal number of boys + number of girls<BR>\n" );
document.write( "60% of (b + g) is boys on the 1st day<BR>\n" );
document.write( "later on, 6 girls leave and 6 boys are added<BR>\n" );
document.write( "That means (b + g) does not change, but boys are now 75% of (b + g)<BR>\n" );
document.write( "so, on the 1st day,<BR>\n" );
document.write( "(a).....b/(b + g) = .60<BR>\n" );
document.write( "and later on,<BR>\n" );
document.write( "(b).....(b + 6)/(b + g) = .75<BR>\n" );
document.write( "solve the first equation for b<BR>\n" );
document.write( "b = .6b + .6g<BR>\n" );
document.write( ".4b = .6g<BR>\n" );
document.write( "b = (3/2)g<BR>\n" );
document.write( "now solve the second equation for g<BR>\n" );
document.write( ".75(b + g) = b + 6<BR>\n" );
document.write( ".75b + .75g = b + 6<BR>\n" );
document.write( ".75g = .25b + 6<BR>\n" );
document.write( "express as fractions<BR>\n" );
document.write( "(3/4)g = (1/4)b + 6<BR>\n" );
document.write( "3g = b + 24<BR>\n" );
document.write( "g = (1/3)b + 8<BR>\n" );
document.write( "substitute b = (3/2)g (from before)<BR>\n" );
document.write( "g = (1/3)(3/2)g + 8<BR>\n" );
document.write( "g = (1/2)g + 8<BR>\n" );
document.write( "2g = g + 16<BR>\n" );
document.write( "g = 16<BR>\n" );
document.write( "now substitute this value in either of the two equations (a) or (b)<BR>\n" );
document.write( "b/(b + 16) = 3/5<BR>\n" );
document.write( "b = (3/5)(b + 16)<BR>\n" );
document.write( "(5/3)b = b + 16<BR>\n" );
document.write( "(2/3)b = 16<BR>\n" );
document.write( "b = (3/2)16<BR>\n" );
document.write( "b = 24<BR>\n" );
document.write( "so, there are 16 girls and 24 boys on the first day of school<BR>\n" );
document.write( "If I add 6 boys and subtract 6 girls like the problems says<BR>\n" );
document.write( "are the boys 75% of (boys + girls)?<BR>\n" );
document.write( "(24 + 6) /((24 + 6) +(16 - 6)) = .75<BR>\n" );
document.write( "30/(30 + 10) = 30/40 = .75<BR>\n" );
document.write( "answer checks\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );