document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170801>Question 1170801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following problems by using elimination or substitution.  Make sure to define your variables, write a system, solve showing all work and write a complete sentence answer.\r<BR>\n" );
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document.write( "Robert has a job offer in which he will receive $900 a month plus a commission of 4.5% of the total price of the cars that he sells.  His current job pays him $1200 a month plus a commission of 3.25% of the total price of the cars that he sells.  How many sales would he need each month to make the new job a better deal?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795684 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=795684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> new job = 900 a month plus 4.5% of the sales.<BR>\n" );
document.write( "old job = 1200 a month plus 3.25% of the sales.\r<BR>\n" );
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document.write( "equation for new job is y = .045 * x + 900<BR>\n" );
document.write( "equation for old job is y = .0325 * x + 1200\r<BR>\n" );
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document.write( "you want to know when the new job gives him better total compensation than the old job.\r<BR>\n" );
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document.write( "this occurs when .045 * x + 900 > .0325 * x + 1200\r<BR>\n" );
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document.write( "subtract 900 from both sides of the inequality and subtract .0325 * x from both sides of the inequality and simplify to get:\r<BR>\n" );
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document.write( ".0125 * x = 300\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 300 / .0125 = 24,000\r<BR>\n" );
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document.write( "the new job will provide better compensation than the old job when sales exceed 24,000.\r<BR>\n" );
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document.write( "to confirm, select sales lower than 24,000, higher than 24,000, and equal to 24,000.\r<BR>\n" );
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document.write( "i picked 20,000, 30,000 and 24,000\r<BR>\n" );
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document.write( "at 20,000 sales, new job pays 900 + .045 * 20,000 = 1800 and old job pays 1200 + .0325 * 20,000 = 1850.<BR>\n" );
document.write( "old job pays better.\r<BR>\n" );
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document.write( "at 30,000 sales, new job pays 900 + .045 * 30,000 = 2250 and old job pays 1200 + .0325 * 30,000 = 2175.<BR>\n" );
document.write( "new job pays better.\r<BR>\n" );
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document.write( "at 24,000 sales, new job pays 900 + .045 * 24,000 = 1980 and old job pays 1200 + .0325 * 24,000 = 1980.<BR>\n" );
document.write( "they pay the same.\r<BR>\n" );
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document.write( "you can graph these equations.<BR>\n" );
document.write( "the graph will show you where the break even point is and when the new job starts paying more than the old job.\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/2020/120101.jpg\" >\r<BR>\n" );
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document.write( "red is the new job, blue is the old job.\r<BR>\n" );
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