document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144362>Question 1144362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Acme Movers charges ​$100 plus ​$40 per hour to move household goods across town.​ Hank's Movers charges ​$65 per hour. For what lengths of time does it cost less to hire​ Hank's Movers?\r<BR>\n" );
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document.write( "It costs less to hire​ Hank's Movers for times less than ___hours. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765428 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=765428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula for acme is y = 40 * x + 100<BR>\n" );
document.write( "formula for hank is y = 65 * x\r<BR>\n" );
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document.write( "hank cost less than acme when 65 * x < 40 * x + 100<BR>\n" );
document.write( "subtract 40 * x from both sides of this equation to get:<BR>\n" );
document.write( "65 * x - 40 * x < 100<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "25 * x < 100<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x < 100 / 25 which becomes x < 4.\r<BR>\n" );
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document.write( "hank will be cheaper than acme when the number of hours required to finish the job is less than 4 hours.\r<BR>\n" );
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document.write( "the two equations for hank and acme can be graphed.<BR>\n" );
document.write( "the graph shows where the break even point and when hank is cheaper and when acme is cheaper.\r<BR>\n" );
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document.write( "the graph is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/082901.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the red line is hank.<BR>\n" );
document.write( "the blue line is acme.\r<BR>\n" );
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document.write( "you can see that the break even point is 4 hours.<BR>\n" );
document.write( "when the number of hours is less than 4, hank is cheaper (red line is below the blue line),<BR>\n" );
document.write( "when the number of hours is greater than 4, acme is cheaper (blue line is below the red line).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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