document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205098>Question 1205098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Devonte is throwing a party to watch the Stanley Cup Finals. He orders pizza that cost $11 each and cartons of wings that cost $9.99 each. With at least 34 people coming over, Devonte spends at least $72.96 and orders a minimum of 7 pizzas and cartons of wings.<BR>\n" );
document.write( "Part A. Write a system of inequalities that describes this situation.<BR>\n" );
document.write( "Part B. Graph the solution set and determine a possible number of pizza and cartons of wings he ordered for his party.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841733 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=841733\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of pizzas.<BR>\n" );
document.write( "y = number of cartons of wings.\r<BR>\n" );
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document.write( "you have two inequalities that need to be solved simultaneously.<BR>\n" );
document.write( "they are:\r<BR>\n" );
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document.write( "x + y >= 7<BR>\n" );
document.write( "11x + 9.99y >= 72.96\r<BR>\n" );
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document.write( "with the desmos.com calculator, you would graph the opposite of the inequalities.<BR>\n" );
document.write( "the area on the graph that is not shaded is your region of feasibility.\r<BR>\n" );
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document.write( "the graph is shown below.\r<BR>\n" );
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document.write( "your corner points are the minimum number of x and y that satisfy the inequality.\r<BR>\n" );
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document.write( "the corner points are in (x,y) format and are equal to (0,7.303), (3,4), (7,0).<BR>\n" );
document.write( "for example, at (0,7.303), x is equal to 0 and y is equal to 7.303).<BR>\n" );
document.write( "the value of y is actually equal to 7.303303303.<BR>\n" );
document.write( "the value on the graph is rounded to 3 decimal places.\r<BR>\n" );
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document.write( "at (0,7.303303303), the inequalities are satisfied because:<BR>\n" );
document.write( "x + y >= 7 becomes 0 + 7.303 = 7.303 >= 7.<BR>\n" );
document.write( "11x + 9.99y >= 72.96 becomes 0 + 9.99*7.303303303 = 72.96 >= 7.96.\r<BR>\n" );
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document.write( "the minimum number of pizzas and cartons of wings becomes:<BR>\n" );
document.write( "0 pizzas and 8 cartons of wings.<BR>\n" );
document.write( "3 pizzas and 4 cartons of wings.<BR>\n" );
document.write( "7 pizzas and 0 cartons of wings.\r<BR>\n" );
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document.write( "any value of x and y on the graph that are not shaded are valid combinations.\r<BR>\n" );
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document.write( "0 pizzas and 8 cartons of wings cost 9.99 * 8 = 79.92 which is greater than or equal to 72.96.<BR>\n" );
document.write( "3 pizzas and 4 cartons of wings cost 3 * 11 + 4 * 9.99 = 72.96 which is greater than or equa to 72.96.<BR>\n" );
document.write( "7 pizzas and 0 cartons of wings cost 7 * 11 = 77 which is greater than or equal to 72.96.<BR>\n" );
document.write( "all inequalities are satisfied.<BR>\n" );
document.write( "x + y >= 7<BR>\n" );
document.write( "11x + 9.99y >= 72.96\r<BR>\n" );
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document.write( "one possible combination is 3 pizzas and 4 cartons of wings that would cost 33 +  39.96 for a total of 72.96 which is greater than or equal to 72.96.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/112501.jpg\">\r<BR>\n" );
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document.write( "as long as x + y >= 7 and 11x + 9.99y >= 72.96, the combination is valid.\r<BR>\n" );
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document.write( "for example, when x + y = 20, any combination of x and y would satisfy the inequality.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "when x = 0 and y = 20, the total cost is 20 * 9.99 which is >= 72.96<BR>\n" );
document.write( "when x = 20 and y = 0, the total cost is 20 * 11 which is >= 72.96<BR>\n" );
document.write( "when x = 10 and y = 10, the total cost is 10 * 11 + 10 * 9.99 which is >= 72.96.\r<BR>\n" );
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