document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=955319>Question 955319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are benches in a class room if 4 students sit on each bench , three benches are left vacant and if 3 students sit on each bench three students are left standing what is the total num of students in the class </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #583531 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=583531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the number of benches.<BR>\n" );
document.write( "let y equal the number of students.\r<BR>\n" );
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document.write( "when there are 4 students to a bench, then there are 3 benches left over.\r<BR>\n" );
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document.write( "this means that y = 4x - 12.\r<BR>\n" );
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document.write( "that formula states that the number of students is equal to 4 times the number of benches - 12 students.\r<BR>\n" );
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document.write( "the 12 students that are subtracted are the 4 students per bench for the 3 benches that are empty.\r<BR>\n" );
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document.write( "when there are 3 students to a bench, then there are 3 students left over.\r<BR>\n" );
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document.write( "this means that y = 3x + 3.\r<BR>\n" );
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document.write( "that formula states that the number of students is equal to 3 times the number of benches plus 3 students.\r<BR>\n" );
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document.write( "the 3 students that are added are the 3 students that could not fit on any of the benches because there were only 3 students per bench.\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "y = 4x - 12<BR>\n" );
document.write( "y = 3x + 3\r<BR>\n" );
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document.write( "in the second equation, substitute 4x - 12 for y and you get:\r<BR>\n" );
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document.write( "4x - 12 = 3x + 3\r<BR>\n" );
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document.write( "solve for x to get x = 15.\r<BR>\n" );
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document.write( "the number of benches has to be 15 if the calculations were done correctly.\r<BR>\n" );
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document.write( "with 4 students per bench, you get 4 * 15 = 60 students.<BR>\n" );
document.write( "since 3 of the benches were empty, you have to subtract 3 * 4 = 12.<BR>\n" );
document.write( "you get 60 - 12 = 48 students.\r<BR>\n" );
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document.write( "with 3 students per bench, you get 3 * 15 = 45 students.<BR>\n" );
document.write( "since 3 of the students couldn't fit on any of the benches, you have to add 3 students to the total.<BR>\n" );
document.write( "you get 45 + 3 = 48 students.\r<BR>\n" );
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document.write( "the solution is 15 benches and 48 students.\r<BR>\n" );
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