document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=487755>Question 487755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Patricia knows that at some point during the calendar year her basic monthly telephone rate increased from $17.10 to $18.40. If she paid a total of $207.80 for basic telephone service for the calendar year, in what month did the rate increase take effect?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333144 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> her total bill was $207.80<BR>\n" );
document.write( "she had x months at a rate of $17.10<BR>\n" );
document.write( "she had y months at a rate of $18.40<BR>\n" );
document.write( "you have 2 equations.<BR>\n" );
document.write( "x + y = 12<BR>\n" );
document.write( "17.10*x + 18.40*y = 207.8<BR>\n" );
document.write( "you need to solve these 2 equations simultaneously to get your answer.<BR>\n" );
document.write( "we'll solve this equation by elimination.<BR>\n" );
document.write( "your equations are:<BR>\n" );
document.write( "x + y = 12 (equation 1)<BR>\n" );
document.write( "17.10x + 18.40y = 207.8 (equation 2)<BR>\n" );
document.write( "multiply both sides of equation 1 by 17.10 to get:<BR>\n" );
document.write( "17.10x + 17.10y = 205.2 (equation 3)<BR>\n" );
document.write( "17.10x + 18.40y = 207.8 (equation 2)<BR>\n" );
document.write( "subtract equation 3 from equation 2 to get:<BR>\n" );
document.write( "1.3y = 2.6<BR>\n" );
document.write( "divide both sides of this equation by 1.3 to get:<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "since x + y = 12, this means that:<BR>\n" );
document.write( "x = 10<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "substitute these values for x and y in equation 2 to get:<BR>\n" );
document.write( "17.10*10 + 18.40*2 = 207.8 which becomes:<BR>\n" );
document.write( "171.0 + 36.8 = 207.8 which becomes:<BR>\n" );
document.write( "207.8 = 207.8<BR>\n" );
document.write( "this confirms the values for x and y are good.<BR>\n" );
document.write( "your answer is:<BR>\n" );
document.write( "she had 10 months at $17.10 and 2 months at $18.40<BR>\n" );
document.write( "the rate increase took effect in November.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );