document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887261>Question 887261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1150 . What was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536522 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=536522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets start off by letting x be the first mechanics rate and y being the second mechanics rate.  We know that the first mechanic worked 5 hours and that the second mechanic worked 10 hours and together they charged 1150.  An equation to express this would be:<br>  \r<BR>\n" );
document.write( "\n" );
document.write( "5x+10y = 1150<br>\r<BR>\n" );
document.write( "\n" );
document.write( "We also know that together they charged 160/per hour.  An equation to express this would be:<br>\r<BR>\n" );
document.write( "\n" );
document.write( "x+y = 160<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Now we can solve the second equation for x or the first mechanics rate.<br>\r<BR>\n" );
document.write( "\n" );
document.write( "x+y = 160<BR>\n" );
document.write( "x = 160 - y<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Now that we have an expression for x we can plug that back into the first equation and solve for y or how much the second mechanic charged.<br>\r<BR>\n" );
document.write( "\n" );
document.write( "5x+10y=1150 plug in x =160-y<BR>\n" );
document.write( "5(160-y)+10y=1150 Distribute<BR>\n" );
document.write( "800 -5y+10y = 1150 Combine like terms<BR>\n" );
document.write( "800 +5y = 1150 Subtract 800 from both sides<BR>\n" );
document.write( "5y = 350 divide by 5<BR>\n" );
document.write( "y = 70<br>\r<BR>\n" );
document.write( "\n" );
document.write( "So we know that the second mechanic charged $70/hour.  We also know that(from our work before) that the first mechanic charges $160 - the rate the second mechanic charged.  We know that's $70/hour so we can plug in and solve for the first rate.<br> \r<BR>\n" );
document.write( "\n" );
document.write( "x = 160-y<BR>\n" );
document.write( "x = 160-70<BR>\n" );
document.write( "x = 90<br>\r<BR>\n" );
document.write( "\n" );
document.write( "So we know that the first mechanic charged $90/hour and the second mechanic charged $70/hour. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );