document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=335954>Question 335954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of math teachers went to a restaurant. They agreed to split the bill equally. When the bill arrived, two of them discovered they had forgotten their money. The others agreed to make up the difference by paying an extra $1.30 each. If the total bill was $78, how many teachers were in the group? \r<BR>\n" );
document.write( "\n" );
document.write( "I figured out the answer is 12 teachers but i can't figure out the equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #240934 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=240934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We don't know how many teachers there are, so let's say that there are 'x' teachers (ie x = # of teachers)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since \"the total bill was $78\" and \"They agreed to split the bill equally\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78%2Fx=c ALIGN=MIDDLE  ALT=\"78%2Fx=c\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=78%2Fx ALIGN=MIDDLE  ALT=\"c=78%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > where 'c' is the amount of money each teacher pays (before the two back out)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since \"two of them discovered they had forgotten their money\" and \"The others agreed to make up the difference by paying an extra $1.30 each\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78%2F%28x-2%29=c%2B1.3 ALIGN=MIDDLE  ALT=\"78%2F%28x-2%29=c%2B1.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Basically, the bill of $78 is now divided among <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2 ALIGN=MIDDLE  ALT=\"x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > teachers and each teacher now pays <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B1.3 ALIGN=MIDDLE  ALT=\"c%2B1.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78%2F%28x-2%29=c%2B1.3 ALIGN=MIDDLE  ALT=\"78%2F%28x-2%29=c%2B1.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78%2F%28x-2%29=78%2Fx%2B1.3 ALIGN=MIDDLE  ALT=\"78%2F%28x-2%29=78%2Fx%2B1.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=78%2Fx ALIGN=MIDDLE  ALT=\"c=78%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78x=78%28x-2%29%2B1.3x%28x-2%29 ALIGN=MIDDLE  ALT=\"78x=78%28x-2%29%2B1.3x%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-2%29 ALIGN=MIDDLE  ALT=\"x%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78x=78x-156%2B1.3x%5E2-2.6x ALIGN=MIDDLE  ALT=\"78x=78x-156%2B1.3x%5E2-2.6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=780x=780x-1560%2B13x%5E2-26x ALIGN=MIDDLE  ALT=\"780x=780x-1560%2B13x%5E2-26x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply every term by 10 to get every number to be a whole number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=780x-1560%2B13x%5E2-26x-780x ALIGN=MIDDLE  ALT=\"0=780x-1560%2B13x%5E2-26x-780x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 780x from both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=13x%5E2-26x-1560 ALIGN=MIDDLE  ALT=\"0=13x%5E2-26x-1560\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x%5E2-26x-1560 ALIGN=MIDDLE  ALT=\"13x%5E2-26x-1560\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BC ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=13 ALIGN=MIDDLE  ALT=\"A=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-26 ALIGN=MIDDLE  ALT=\"B=-26\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-1560 ALIGN=MIDDLE  ALT=\"C=-1560\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's use the quadratic formula to solve for \"x\":\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-26%29+%2B-+sqrt%28+%28-26%29%5E2-4%2813%29%28-1560%29+%29%29%2F%282%2813%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-26%29+%2B-+sqrt%28+%28-26%29%5E2-4%2813%29%28-1560%29+%29%29%2F%282%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=13 ALIGN=MIDDLE  ALT=\"A=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-26 ALIGN=MIDDLE  ALT=\"B=-26\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-1560 ALIGN=MIDDLE  ALT=\"C=-1560\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+%2B-+sqrt%28+%28-26%29%5E2-4%2813%29%28-1560%29+%29%29%2F%282%2813%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2826+%2B-+sqrt%28+%28-26%29%5E2-4%2813%29%28-1560%29+%29%29%2F%282%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-26 ALIGN=MIDDLE  ALT=\"-26\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26 ALIGN=MIDDLE  ALT=\"26\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+%2B-+sqrt%28+676-4%2813%29%28-1560%29+%29%29%2F%282%2813%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2826+%2B-+sqrt%28+676-4%2813%29%28-1560%29+%29%29%2F%282%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-26 ALIGN=MIDDLE  ALT=\"-26\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=676 ALIGN=MIDDLE  ALT=\"676\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+%2B-+sqrt%28+676--81120+%29%29%2F%282%2813%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2826+%2B-+sqrt%28+676--81120+%29%29%2F%282%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2813%29%28-1560%29 ALIGN=MIDDLE  ALT=\"4%2813%29%28-1560%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-81120 ALIGN=MIDDLE  ALT=\"-81120\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+%2B-+sqrt%28+676%2B81120+%29%29%2F%282%2813%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2826+%2B-+sqrt%28+676%2B81120+%29%29%2F%282%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28676--81120%29 ALIGN=MIDDLE  ALT=\"sqrt%28676--81120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28676%2B81120%29 ALIGN=MIDDLE  ALT=\"sqrt%28676%2B81120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+%2B-+sqrt%28+81796+%29%29%2F%282%2813%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2826+%2B-+sqrt%28+81796+%29%29%2F%282%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=676 ALIGN=MIDDLE  ALT=\"676\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81120 ALIGN=MIDDLE  ALT=\"81120\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81796 ALIGN=MIDDLE  ALT=\"81796\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+%2B-+sqrt%28+81796+%29%29%2F%2826%29 ALIGN=MIDDLE  ALT=\"x+=+%2826+%2B-+sqrt%28+81796+%29%29%2F%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26 ALIGN=MIDDLE  ALT=\"26\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+%2B-+286%29%2F%2826%29 ALIGN=MIDDLE  ALT=\"x+=+%2826+%2B-+286%29%2F%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81796 ALIGN=MIDDLE  ALT=\"81796\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=286 ALIGN=MIDDLE  ALT=\"286\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+%2B+286%29%2F%2826%29 ALIGN=MIDDLE  ALT=\"x+=+%2826+%2B+286%29%2F%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2826+-+286%29%2F%2826%29 ALIGN=MIDDLE  ALT=\"x+=+%2826+-+286%29%2F%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28312%29%2F%2826%29 ALIGN=MIDDLE  ALT=\"x+=+%28312%29%2F%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-260%29%2F%2826%29 ALIGN=MIDDLE  ALT=\"x+=++%28-260%29%2F%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12 ALIGN=MIDDLE  ALT=\"x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-10 ALIGN=MIDDLE  ALT=\"x+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the possible solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12 ALIGN=MIDDLE  ALT=\"x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-10 ALIGN=MIDDLE  ALT=\"x+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "Ignore the negative solution as a negative amount of teachers makes no sense.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So there are originally 12 teachers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">website</a>. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Jim </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );