document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208844>Question 1208844</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Mike works at a grocery store and delivers newspapers. He earns $7 per hour at the grocery store and $10 per hour delivering newspapers. He can work no more than 20 hours per week. Graph two inequalities that Mike can use to determine how many hours he needs to work at each job to earn at least $90. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847329 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=847329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = number of hours worked at the grocery store<BR>\n" );
document.write( "y = number of hours delivering newspapers\r<BR>\n" );
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document.write( "The two inequalities Mike would graph are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By+%3C=+20%2C7x%2B10y+%3E=+90%29 ALIGN=MIDDLE  ALT=\"system%28x%2By+%3C=+20%2C7x%2B10y+%3E=+90%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The first inequality is the constraint where Mike is able to work at most 20 hours, i.e. 20 hours or fewer.<BR>\n" );
document.write( "The other inequality is making his total earnings (7x+10y dollars) to be $90 or larger.<BR>\n" );
document.write( "7x = amount earned just from the grocery store<BR>\n" );
document.write( "10y = amount earned from delivering newspapers\r<BR>\n" );
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document.write( "The line x+y = 20 goes through (0,20) and (20,0). <BR>\n" );
document.write( "We shade below this line to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By+%3C=+20 ALIGN=MIDDLE  ALT=\"x%2By+%3C=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This boundary line is solid because of the \"or equal to\".\r<BR>\n" );
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document.write( "The line 7x+10y = 90 goes through (0,9) and (10,2). We shade below above line to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B10y+%3E=+90 ALIGN=MIDDLE  ALT=\"7x%2B10y+%3E=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This boundary is also solid.\r<BR>\n" );
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document.write( "These two regions overlap to help form the solution set. <BR>\n" );
document.write( "This is denoted as region R shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28500%2C500%2C-5%2C25%2C-5%2C25%2C%0D%0Agraph%28500%2C500%2C-5%2C25%2C-5%2C25%2C-100%2C-x%2B20%2C%2890-7x%29%2F10%29%2C%0D%0Alocate%284.5%2C10%2C%22R%22%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x+y = 20 is the green line<BR>\n" );
document.write( "7x+10y = 90 is the blue line\r<BR>\n" );
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document.write( "We focus only on the upper right quadrant where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+0 ALIGN=MIDDLE  ALT=\"x+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E=+0 ALIGN=MIDDLE  ALT=\"y+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > since it makes no sense to have x or y be negative. <BR>\n" );
document.write( "Region R is a quadrilateral with these vertex points<BR>\n" );
document.write( "(0,9), (0,20), (20,0), (12.8571, 0)<BR>\n" );
document.write( "The decimal value is approximate.\r<BR>\n" );
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document.write( "A few selected points in region R would be:<BR>\n" );
document.write( "(2, 13), (5, 10), and (9, 9)<BR>\n" );
document.write( "I'll let the student verify each point with the constraint inequalities.\r<BR>\n" );
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document.write( "A point like (4,16) is on a solid boundary line, which means we include it as part of the solution set.\r<BR>\n" );
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document.write( "A point like (5,22) is not inside region R, and not on the boundary either, so it's not a solution point. <BR>\n" );
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