document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118568>Question 1118568</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are buying movie passes and gift certificates as prizes for an event. You need at least 5 movie passes and 2 gift certificates. A movie pass costs $6 and a gift certificate cost $10. The most you can spend is $70. \r<BR>\n" );
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document.write( "a) Write a system of linear inequalities that shoes the number of movie passes x and gift certificates y that can be purchased.<BR>\n" );
document.write( "b) Graph the system<BR>\n" );
document.write( "c) Use the graph to determine if you can buy 6 movie passes and 3 gift certificates.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733927 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=733927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of movie passes.<BR>\n" );
document.write( "let y = number of gift certificates.\r<BR>\n" );
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document.write( "you need at least 5 movie passes, so x >= 5.\r<BR>\n" );
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document.write( "you need at least 2 gift certificates, so y >= 2.\r<BR>\n" );
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document.write( "a movie pass costs 6 dollars and a gift certificate costs 10 dollars and the most ou can spend is 70 dollars, so 6x + 10y <= 70.\r<BR>\n" );
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document.write( "your system of requirements are:\r<BR>\n" );
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document.write( "x >= 5<BR>\n" );
document.write( "y >= 2<BR>\n" );
document.write( "6x + 10y <= 70\r<BR>\n" );
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document.write( "when x = 6 and y = 3, 6x + 10y <= 70 becomes 6*6 + 10*3 <= 70 which becomes 36 + 30 <= 70 which becomes 66 <= 70 which is true.\r<BR>\n" );
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document.write( "therefore, you can buy 6 movie passes and 3 gift certificates and still stay under the limit of 70 dollars.\r<BR>\n" );
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document.write( "the following graph shows that.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/061302.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "in this graph, the opposite of the constraint inequalities are graphed.\r<BR>\n" );
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document.write( "the area of the graph that is not shaded is the region of feasibility.\r<BR>\n" );
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document.write( "6 movie passes and 3 gift certificates is the intersection of the line x = 6 and y = 3.\r<BR>\n" );
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document.write( "that intersection is in the portion of the graph that is not shaded.\r<BR>\n" );
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document.write( "this means that 6 movie passes and 3 gift certificates are within the constraints of the problem.\r<BR>\n" );
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document.write( "this was shown algebraically above the graph.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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