document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191485>Question 1191485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Translate to a system of inequalities and solve.<BR>\n" );
document.write( "Jocelyn is pregnant and needs to eat at least 400 more calories a day than usual. When buying groceries one day with a budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150 calories each. The bananas cost $0.35 each and the granola bars cost $2.50 each.<BR>\n" );
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document.write( "Write a system of inequalities to model this situation. (Let b represent the bananas bought and let g represent the number of granola bars bought. Enter your answers as a comma-separated list of inequalities.)<BR>\n" );
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document.write( "Graph the system.<BR>\n" );
document.write( "(c)<BR>\n" );
document.write( "Could she buy 6 bananas and 6 granola bars?<BR>\n" );
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document.write( "Could she buy 3 bananas and 3 granola bars? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823266 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=823266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's your graph.\r<BR>\n" );
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document.write( "using the desmos.com graph, you graph the opposite of the inequalities.<BR>\n" );
document.write( "the area of the graph that is not shaded is your region of feasibility.<BR>\n" );
document.write( "that and the points on the line if the inequalities are <= or >=, rather than < or >.\r<BR>\n" );
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document.write( "you can see from the graph that the point (0,6) is one of the corner points of the feasible region.\r<BR>\n" );
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document.write( "answers to your questions are below:\r<BR>\n" );
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document.write( "(a)<BR>\n" );
document.write( "Write a system of inequalities to model this situation. (Let b represent the bananas bought and let g represent the number of granola bars bought. Enter your answers as a comma-separated list of inequalities.)\r<BR>\n" );
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document.write( "the inequalities are:<BR>\n" );
document.write( ".35x + 2.5y <= 15<BR>\n" );
document.write( "90x + 150y >= 400<BR>\n" );
document.write( "first equation models the cost.<BR>\n" );
document.write( "second equation models the calories.\r<BR>\n" );
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document.write( "(b)<BR>\n" );
document.write( "Graph the system.\r<BR>\n" );
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document.write( "done.\r<BR>\n" );
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document.write( "(c)<BR>\n" );
document.write( "Could she buy 6 bananas and 6 granola bars?\r<BR>\n" );
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document.write( "no, she cannot buy 6 bananas and 6 granola bars.<BR>\n" );
document.write( "you can see from the graph that the point (6,6) is not in the region of feasibility.<BR>\n" );
document.write( "an evaluation of the equations at (6,6) shows you why.<BR>\n" );
document.write( ".35x + 2.5y = 17.1 which is not less than or equal to 15.<BR>\n" );
document.write( "90x + 150y = 1440 which is greater than 400.<BR>\n" );
document.write( "first constraint is not satisfied.<BR>\n" );
document.write( "second constraint is.<BR>\n" );
document.write( "both must be satisfied, otherwise the point is not valid.\r<BR>\n" );
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document.write( "(d)<BR>\n" );
document.write( "Could she buy 3 bananas and 3 granola bars?\r<BR>\n" );
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document.write( "yes, she can buy 3 banancas and 3 granola bars.<BR>\n" );
document.write( "you can see from the graph that the point (3,3) is in the region of feasibility.<BR>\n" );
document.write( "an evaluation of the inequalities will show that they are both true.<BR>\n" );
document.write( ".35x + 2.5y = 8.55 which is less than 15.<BR>\n" );
document.write( "90x + 1.5y = 720 which is greater than 400.<BR>\n" );
document.write( "both constraints are satisfied as they need to be for the point to be feasible.\r<BR>\n" );
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document.write( "let me know if you have any questions or concerns.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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