document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171637>Question 1171637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine when the cost of the two services will be the same amount, and what the price will be.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The Strauss family is deciding between two lawn-care services. Green Lawn charges a $51 startup fee plus $27 per month. Yard Guard charges a $26 startup fee plus $32 per month. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796539 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=796539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> green lawn equation is a = 51 + 27x<BR>\n" );
document.write( "yard guard equation is b = 26 + 32x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they will be equal when a = b.<BR>\n" );
document.write( "this happens when 51 + 27x = 26 + 32x.<BR>\n" );
document.write( "subtract 26 from both sides of that equation and subtract 27x from both sides of that equation to get:<BR>\n" );
document.write( "51 - 26 = 32x - 27x<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "25 = 5x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 25/5 = 5<BR>\n" );
document.write( "confirm by replacing x with 5 in both equations to get:<BR>\n" );
document.write( "51 + 27*5 = 26 + 32*5<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "186 = 186, confirming the value of x is good.<BR>\n" );
document.write( "your solution is that the cost will be the same in 5 months.<BR>\n" );
document.write( "after that point, the lawn service that charges 51 + 27 per month will be cheaper.<BR>\n" );
document.write( "this can be seen on the following graph.<BR>\n" );
document.write( "y = 51 + 27x is in red.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/121101.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );