document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185026>Question 185026</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Teacher generated question, not from a textbook.\r<BR>\n" );
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document.write( "You are in charge of setting up a room for an awards banquet at your school.  A total of 122 people will attend the banquet.  The school has tables that seat either 8 or 10 people.  No empty seats are allowed.  How many of each size table will you need to use to make sure everyone has a seat?\r<BR>\n" );
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document.write( "Can get to \"8x + 10y = 122\" but need to develop second equation to solve using elimination or substitution.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138827 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Teacher generated question, not from a textbook.<BR>\n" );
document.write( "You are in charge of setting up a room for an awards banquet at your school.<BR>\n" );
document.write( " A total of 122 people will attend the banquet. The school has tables that seat<BR>\n" );
document.write( " either 8 or 10 people. No empty seats are allowed. How many of each size table<BR>\n" );
document.write( " will you need to use to make sure everyone has a seat?<BR>\n" );
document.write( "Can get to \"8x + 10y = 122\" but need to develop second equation to solve<BR>\n" );
document.write( " using elimination or substitution.<BR>\n" );
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document.write( "That's the only equation you will get from the information given, however since<BR>\n" );
document.write( "there are no empty seats, x and y have to be integers that will give 122.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "simplify the equation by dividing by 2, re-write it:<BR>\n" );
document.write( "4x + 5y = 61<BR>\n" );
document.write( "5y = 61 - 4x<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2F5 ALIGN=MIDDLE  ALT=\"61%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >x<BR>\n" );
document.write( "choose a value for x and see if y is an integer, if it is that is a one solution<BR>\n" );
document.write( "I found there are three solutions<BR>\n" );
document.write( "x=4<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2F5 ALIGN=MIDDLE  ALT=\"61%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >(4)<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2F5 ALIGN=MIDDLE  ALT=\"61%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F5 ALIGN=MIDDLE  ALT=\"16%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F5 ALIGN=MIDDLE  ALT=\"45%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 9; (32 + 90 = 122)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2F5 ALIGN=MIDDLE  ALT=\"61%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >(9)<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2F5 ALIGN=MIDDLE  ALT=\"61%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F5 ALIGN=MIDDLE  ALT=\"36%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >x<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F5 ALIGN=MIDDLE  ALT=\"25%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 5; (72 + 40 = 122)<BR>\n" );
document.write( "and one more<BR>\n" );
document.write( "x=14<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2F5 ALIGN=MIDDLE  ALT=\"61%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >(14)<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61%2F5 ALIGN=MIDDLE  ALT=\"61%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56%2F5 ALIGN=MIDDLE  ALT=\"56%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F5 ALIGN=MIDDLE  ALT=\"5%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 1; (112 +10 = 122)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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