document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209934>Question 1209934</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 #851083 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's use variables to represent the daily wages:\r<BR>\n" );
document.write( "\n" );
document.write( "* Let 't' represent the daily wage of a technician.<BR>\n" );
document.write( "* Let 'a' represent the daily wage of an apprentice.\r<BR>\n" );
document.write( "\n" );
document.write( "We can set up two equations based on the given information:\r<BR>\n" );
document.write( "\n" );
document.write( "**Equation 1:** 7 technicians and 3 apprentices earn 820.<BR>\n" );
document.write( "   * 7t + 3a = 820\r<BR>\n" );
document.write( "\n" );
document.write( "**Equation 2:** If one apprentice becomes a technician, there are 8 technicians and 2 apprentices, and they earn 880.<BR>\n" );
document.write( "   * 8t + 2a = 880\r<BR>\n" );
document.write( "\n" );
document.write( "Now we have a system of two linear equations with two variables. We can solve for 't' and 'a'.\r<BR>\n" );
document.write( "\n" );
document.write( "**Solve the System of Equations:**\r<BR>\n" );
document.write( "\n" );
document.write( "We can use the substitution or elimination method. Let's use the elimination method.\r<BR>\n" );
document.write( "\n" );
document.write( "1.  Multiply Equation 1 by 2 and Equation 2 by 3 to make the 'a' coefficients match:<BR>\n" );
document.write( "    * (7t + 3a = 820) * 2  =>  14t + 6a = 1640<BR>\n" );
document.write( "    * (8t + 2a = 880) * 3  =>  24t + 6a = 2640\r<BR>\n" );
document.write( "\n" );
document.write( "2.  Subtract the first modified equation from the second modified equation to eliminate 'a':<BR>\n" );
document.write( "    * (24t + 6a) - (14t + 6a) = 2640 - 1640<BR>\n" );
document.write( "    * 10t = 1000\r<BR>\n" );
document.write( "\n" );
document.write( "3.  Solve for 't':<BR>\n" );
document.write( "    * t = 1000 / 10<BR>\n" );
document.write( "    * t = 100\r<BR>\n" );
document.write( "\n" );
document.write( "4.  Substitute the value of 't' back into either Equation 1 or Equation 2 to solve for 'a'. Let's use Equation 1:<BR>\n" );
document.write( "    * 7(100) + 3a = 820<BR>\n" );
document.write( "    * 700 + 3a = 820<BR>\n" );
document.write( "    * 3a = 820 - 700<BR>\n" );
document.write( "    * 3a = 120\r<BR>\n" );
document.write( "\n" );
document.write( "5.  Solve for 'a':<BR>\n" );
document.write( "    * a = 120 / 3<BR>\n" );
document.write( "    * a = 40\r<BR>\n" );
document.write( "\n" );
document.write( "**Answers:**\r<BR>\n" );
document.write( "\n" );
document.write( "* The daily wage of a technician (t) is $100.<BR>\n" );
document.write( "* The daily wage of an apprentice (a) is $40.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );