document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118379>Question 1118379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an employment agency specializing in temporary construction help pays heavy equipment operators $1.20 per day and general laborers $91 per day if thirty-one people were hired and the payroll was $3339 how many heavy equipment operators were employed? how many laborers<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 #733672 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13209)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "It would be a good idea for you to look at what you have written before you send your question to us.  $1.20 a day for heavy equipment operators?  I don't think anybody would take that job.<br><BR>\n" );
document.write( "So the real rate is clearly supposed to be $120 per day.  Then we have<BR>\n" );
document.write( "x heavy equipment operators at $120 per day and y general laborers at $91 per day, making 31 workers with a total pay of $3339 per day.  Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By+=+31 ALIGN=MIDDLE  ALT=\"x%2By+=+31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120x%2B91y+=+3339 ALIGN=MIDDLE  ALT=\"120x%2B91y+=+3339\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Unfortunately, when we try to solve that system of equations, we don't get answers that are whole numbers.  So even after correcting your $1.20 per day to $120 per day, there is a flaw in your statement of the problem.<br><BR>\n" );
document.write( "When I first read the problem, it occurred to me that we could solve the problem with logical analysis using only the total pay, without knowing the total number of workers.<br><BR>\n" );
document.write( "Looking at the equation for total pay, we can see that the total pay for the heavy equipment operators will be a multiple of $10.  Since the total pay is $3339 and the daily pay for the general laborers is $91, the number of general laborers must be a number ending in 9.<br><BR>\n" );
document.write( "Then we could try 9, 19, 29,... as the number of general laborers and see which gives us a whole number for the number of heavy equipment operators.<br><BR>\n" );
document.write( "But we can be even a little smarter than that.  The total pay, $3339, is a multiple of 3, and the daily pay for the heavy equipment operators is a multiple of 3.  Since the $91 daily pay for the general laborers is NOT a multiple of 3, the number of general laborers MUST be a multiple of 3.<br><BR>\n" );
document.write( "That means the number of general laborers is either 9, or 39, or 69, or....  With the total pay being $3339, the only number that works is 9.<br><BR>\n" );
document.write( "That gives us 9($91) = $819 for the total pay for the general laborers, leaving $3339-$819 = $2520 as the total pay for the heavy equipment operators.  At $120 per day, the number of heavy equipment operators is then $2520/$120 = 21.<br><BR>\n" );
document.write( "So the total number of workers is 9+21 = 30 -- NOT 31, as you say in your statement of the problem. </SPAN>\n" );
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