document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174699>Question 1174699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mother's weekly budget for fish and chicken is at most Php 1,200. Note that 1 kilogram of fish costs Php<BR>\n" );
document.write( "60 while 1 kilogram of chicken costs Php 120.\r<BR>\n" );
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document.write( "a. Write a system of inequalities for the given situation then graph the solution set of the system.\r<BR>\n" );
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document.write( "b. Determine if the ordered pair (10,7) is a solution to the system. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800158 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=800158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your inequality is 60x + 120y <= 1200.\r<BR>\n" );
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document.write( "x = the number of kilograms of fish.<BR>\n" );
document.write( "y = the number of kilograms of chicken.\r<BR>\n" );
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document.write( "two other inequalities that need to be observed are:\r<BR>\n" );
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document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
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document.write( "when x = 0, the inequality becomes 120y <= 1200.<BR>\n" );
document.write( "solve for y to get y <= 1200/120.<BR>\n" );
document.write( "simplify that to get:<BR>\n" );
document.write( "y <= 10\r<BR>\n" );
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document.write( "when y = 0, the inequality becomes 60x <= 1200.<BR>\n" );
document.write( "solve for x to get x <= 1200/60.<BR>\n" );
document.write( "simplify that to get:<BR>\n" );
document.write( "x <= 20\r<BR>\n" );
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document.write( "it appears that you have a range of values where the inequality of 60x + 120y <= 1200 is true.\r<BR>\n" );
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document.write( "those ranges are:\r<BR>\n" );
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document.write( "0 <= x <= 20<BR>\n" );
document.write( "0 <= y <= 10\r<BR>\n" );
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document.write( "the inequality of 60x + 120y <= 1200 can be graphed.<BR>\n" );
document.write( "using the desmos.com calculator, you would graph the inequality of 60x + 120y >= 1200.\r<BR>\n" );
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document.write( "you would also graph the inequality of x <= 0 and y <= 0.\r<BR>\n" );
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document.write( "all these inequalities being graphed are opposite the inequalities of the problem.\r<BR>\n" );
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document.write( "60x + 120y <= 1200 is graphed as 60x + 120y >= 1200<BR>\n" );
document.write( "x >= 0 is graphed as x <= 0.<BR>\n" );
document.write( "y >= 0 is graphed as y <= 0.\r<BR>\n" );
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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( "any value of (x,y) that is on the line of the equation of 60x + 120y = 1200 or on the line x = 0 and between the points (0,0) and (20,0) or on the line<BR>\n" );
document.write( "y = 0 and between the points (0,0) and (0,20) or in the area of the graph that is not shaded is a valid point of the system of inequalities.\r<BR>\n" );
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document.write( "the graph looks like this.\r<BR>\n" );
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document.write( "from the graph, you can see that the point (10,7) is not part of the solution set because it is in the area of the graph that is shaded.\r<BR>\n" );
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document.write( "when x = 10 and y = 7, the inequality becomes:<BR>\n" );
document.write( "(60 * 10) + (120 * 7) <= 1200 which becomes:<BR>\n" );
document.write( "600 + 840 <= 1200 which becomes:<BR>\n" );
document.write( "1440 <= 1200 which is not true.\r<BR>\n" );
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