document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162334>Question 162334</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> For a recent job, a plumber earned $28/h, and the plumber's apprentice earned $15/h.  The plumber worked 3 hours more than the apprentice.  If together they were paid $213, how much did each earn? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119649 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=119649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let P = number of hours that the plumber worked.<BR>\n" );
document.write( "let H = number of hours that the helper worked.<BR>\n" );
document.write( "since the plumber worked 3 more hours than the helper, the equation for hours worked is<BR>\n" );
document.write( "P = H + 3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the plumber earned 28 dollars per hour and the helper earned 15 dollars per hour, the equation for amount of money each made is the number of hours each worked times the dollars per hour each earned.<BR>\n" );
document.write( "this equation is<BR>\n" );
document.write( "(28*P) + (15*H) = 213 dollars<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "couple of ways to solve this.<BR>\n" );
document.write( "both get the same answer.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "first way<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute for P in the money equation since P is the same as H + 3.<BR>\n" );
document.write( "equation becomes<BR>\n" );
document.write( "(28*(H+3)) + (15*H) = 213<BR>\n" );
document.write( "solve for H.<BR>\n" );
document.write( "28*H + 28*3 + 15*H = 213<BR>\n" );
document.write( "43*H + 84 = 213<BR>\n" );
document.write( "43*H = 129<BR>\n" );
document.write( "H = 3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if H = 3, then P = 6 because P = H + 3.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "6*28 + 3*15 = 213 so your answer is <BR>\n" );
document.write( "Plumber works 6 hours <BR>\n" );
document.write( "Helper works 3 hours.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the other way to solve this is to make both equations in the same form and then solve them simultaneously as follows<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "P = H + 3 is transformed to become<BR>\n" );
document.write( "P - H = 3<BR>\n" );
document.write( "you need to solve<BR>\n" );
document.write( "P - H = 3<BR>\n" );
document.write( "and<BR>\n" );
document.write( "28*P + 15*H = 213<BR>\n" );
document.write( "simultaneously.<BR>\n" );
document.write( "multiply the P - H equation by 28 so you can remove one of the unknowns.<BR>\n" );
document.write( "your equations become<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "28*P - 28*H = 28*3<BR>\n" );
document.write( "28*P + 15*H = 213<BR>\n" );
document.write( "subtracting the top equation from the bottom equation and you get<BR>\n" );
document.write( "0*P + 43*H = 213 - 84 equals<BR>\n" );
document.write( "43*H = 129<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "H = 3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you get the same answer once you solve for P as before.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );