document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142630>Question 142630</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1592009425/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this problem,\r<BR>\n" );
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document.write( "An employment agency pays heavy equipment operators $136.00 a day and general laborers $81 a day. If thirty people were hired and the payroll was $3391, how many heavy equipment operators were employed? How many laborers?\r<BR>\n" );
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document.write( "Thanks in advance for your help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103810 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm presuming that the <b><i> daily</b></i> payroll is $3391.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the number of heavy equipment operators and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the number of general laborers.  We are given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Bg=30 ALIGN=MIDDLE  ALT=\"h%2Bg=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since heavy equipment operators earn $136 per day, the amount of heavy equipment operator payroll is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=136h ALIGN=MIDDLE  ALT=\"136h\"   DISABLED_style= \"max-width:90%; height:auto;\" > per day.  Likewise, the amount of general laborer payroll is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81g ALIGN=MIDDLE  ALT=\"81g\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since the total payroll is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3391 ALIGN=MIDDLE  ALT=\"3391\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=136h%2B81g=3391 ALIGN=MIDDLE  ALT=\"136h%2B81g=3391\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Another way to express the first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=30-g ALIGN=MIDDLE  ALT=\"h=30-g\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Now we can combine the two equations by substitution, that is, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30-g ALIGN=MIDDLE  ALT=\"30-g\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the second equation, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=136%2830-g%29%2B81g=3391 ALIGN=MIDDLE  ALT=\"136%2830-g%29%2B81g=3391\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve this equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the number of general laborers, then subtract that from 30 to get the number of heavy equipment operators.\r<BR>\n" );
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document.write( "The problem you will face once you get the answer is that there is no integer solution to this problem.  The employment agency is going to have a difficult time hiring fractional people.  On the other hand, if you made a typo in the problem statement and actually meant that the general laborers were paid <b><i> $83</b></i> per day, then it works out. (you will need to solve: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=136%2830-g%29%2B83g=3391 ALIGN=MIDDLE  ALT=\"136%2830-g%29%2B83g=3391\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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