document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209933>Question 1209933</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a firm hires 7 technicians and 3 apprentices for total daily wages of 820. if one apprentice is appointed to a technician, the total daily wages become 880. What are thr daily wages for a technician and an apprentice </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851094 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=851094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The AI solution from the other \"tutor\" solves the problem using a standard formal algebraic process, which is of course fine.<br><BR>\n" );
document.write( "This is an example of a problem that can be solved by logical analysis that corresponds to a non-standard algebraic process.<br><BR>\n" );
document.write( "When there were 7 technicians and 3 apprentices, the total wages was 820; when one of the apprentices became a technician, the total wages was 880.<br><BR>\n" );
document.write( "So when one apprentice becomes a technician, the total wages increases by 60.<br><BR>\n" );
document.write( "With that start, suppose now the other two apprentices became technicians.  When there are 9 technicians and 1 apprentice the total wages will be 940, and when there are 10 technicians and no apprentices, the total wages will be 1000.<br><BR>\n" );
document.write( "That of course means the wage of each technician is 1000/10 = 100.<br><BR>\n" );
document.write( "So when the wages for 7 technicians and 3 apprentices was 820, the wages for the 7 technicians was 700, which means the wages for the 3 apprentices was 820-700 = 120; so the wages for each apprentice is 120/3 = 40.<br><BR>\n" );
document.write( "ANSWER: 100 for each technician; 40 for each apprentice.<br><BR>\n" );
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