document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=895979>Question 895979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help converting a word problem into an algebraic equation<BR>\n" );
document.write( "here is the problem<BR>\n" );
document.write( "1 table seats 5 people<BR>\n" );
document.write( "2 tables seat 8 people<BR>\n" );
document.write( "3 tables seat 11 people<BR>\n" );
document.write( "how many people will 12 tables seat?<BR>\n" );
document.write( "Marsha thinks that if she has to set up the conference room with tables to seat 39 people she will need 12 tables. show why she is wrong<BR>\n" );
document.write( "create a model for this situation<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 #543133 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=543133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each time you're adding 3 (5 to 8, 8 to 11)\r<BR>\n" );
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document.write( "So the rate of change is 3 people per table, which represents the slope.\r<BR>\n" );
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document.write( "So m = 3/1 = 3\r<BR>\n" );
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document.write( "Let x = number of tables, y = number of people\r<BR>\n" );
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document.write( "\"1 table seats 5 people\" means x = 1, y = 5\r<BR>\n" );
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document.write( "y = mx+b\r<BR>\n" );
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document.write( "y = 3x+b\r<BR>\n" );
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document.write( "5 = 3*1+b\r<BR>\n" );
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document.write( "5 = 3+b\r<BR>\n" );
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document.write( "5-3 = b\r<BR>\n" );
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document.write( "2 = b\r<BR>\n" );
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document.write( "b = 2\r<BR>\n" );
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document.write( "So the model is y = 3x+2\r<BR>\n" );
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document.write( "Notice how if we have 3 tables for instance, then x = 3\r<BR>\n" );
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document.write( "y = 3x+2\r<BR>\n" );
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document.write( "y = 3*3+2\r<BR>\n" );
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document.write( "y = 11\r<BR>\n" );
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document.write( "which reflects the fact \"3 tables seat 11 people\"\r<BR>\n" );
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document.write( "If we have 39 people, then y = 39. Let's find x\r<BR>\n" );
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document.write( "y = 3x+2\r<BR>\n" );
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document.write( "39 = 3x+2\r<BR>\n" );
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document.write( "39-2 = 3x\r<BR>\n" );
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document.write( "37 = 3x\r<BR>\n" );
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document.write( "3x = 37\r<BR>\n" );
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document.write( "x = 37/3\r<BR>\n" );
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document.write( "x = 12.3333...\r<BR>\n" );
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document.write( "Round that up to go from 12.3333.... to 13\r<BR>\n" );
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document.write( "You'll need 13 tables. Twelve of those tables will have 3*12+2 = 38 people and that last table (the thirteenth table) will have 39-38 = 1 person. \r<BR>\n" );
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document.write( "Of course, you can move people around and have the structure of some tables different, but overall you need 13 tables.\r<BR>\n" );
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document.write( "If she had just 12 tables, then one person would be left out. </SPAN>\n" );
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