document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131934>Question 131934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up, so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involved in the project initially.<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 #96324 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=96324\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let x=total number of boys and girls in the initial project\r<BR>\n" );
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document.write( "Then 0.6x=number of boys<BR>\n" );
document.write( "And 0.4x= number of girls\r<BR>\n" );
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document.write( "Now we know that:\r<BR>\n" );
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document.write( "0.6x+6=0.75x  subtract 0.6x from each side<BR>\n" );
document.write( "0.6x-0.6x+6=0.75x-0.6x  collect like terms\r<BR>\n" );
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document.write( "0.15x=6  divide both sides by 0.15\r<BR>\n" );
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document.write( "x=40 total number of boys and girls in the initial project<BR>\n" );
document.write( "Number of boys=0.6*40=24<BR>\n" );
document.write( "Number of girls=0.4*40=16<BR>\n" );
document.write( "24+16=40\r<BR>\n" );
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document.write( "16-6=10 ----number of girls in the final project<BR>\n" );
document.write( "10=25% of 40\r<BR>\n" );
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document.write( "24+6=30 number of boys in the final project<BR>\n" );
document.write( "30=75% of 40\r<BR>\n" );
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document.write( "Another way (looking at the girls)\r<BR>\n" );
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document.write( "0.4x-6=0.25x  subtract 0.4x from each side\r<BR>\n" );
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document.write( "0.4x-0.4x-6=0.25x-0.4x  collect like terms\r<BR>\n" );
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document.write( "-6=-0.15x  divide both sides by -0.15\r<BR>\n" );
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document.write( "x=40 ----------total number of boys and girls in the initial project\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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