document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=94777>Question 94777</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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69000 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=69000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=the number of boys and girls involved in the project initially<BR>\n" );
document.write( "Then 0.6x=number of boys involved initially<BR>\n" );
document.write( "And 0.4x=number of girls involved initially\r<BR>\n" );
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document.write( "When the professor made changes in the group, he added six boys and subtracted six girls thus the total number (x) remained the same.  So now we have:\r<BR>\n" );
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document.write( "0.6x+6=number of boys involved after the changes<BR>\n" );
document.write( "---and this equals 0.75x<BR>\n" );
document.write( "0.4x-6=number of girls involved after the changes<BR>\n" );
document.write( "---and this equals 0.25x\r<BR>\n" );
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document.write( "So we have two equations, either of which will yield the correct answer<BR>\n" );
document.write( "We'll solve the first one:<BR>\n" );
document.write( "0.6x+6=0.75x<BR>\n" );
document.write( "0.15x=6<BR>\n" );
document.write( "x=40--------------------number of boys and girls involved in the project initially <BR>\n" );
document.write( "0.6x=0.6(40)=24-----------------number of boys\r<BR>\n" );
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document.write( "40-24=16------------------------number of girls\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "24+6=30 which is 75% of 40\r<BR>\n" );
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document.write( "16-6=10 which is 25% of 40\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
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