document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=944205>Question 944205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me, please. \r<BR>\n" );
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document.write( "Tickets for a plane cost 250 pesos for adults and 200 pesos for children. The sponsor of the show collected a total amount of not more than 44,000 pesos from more than 150 adults and children who watched the plane. \r<BR>\n" );
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document.write( "a. How can you find the possible number of children and adults who watched the plane?<BR>\n" );
document.write( "b. Give 4 possible numbers of adults and children who watched the plane. Justify your answers.<BR>\n" );
document.write( "c. The sponsor of the tickets realized that if the prices of the tickets were reduced, more people would have watched the plane. If you were the sponsor of the plane, would you reduce the prices of the tickets? Why? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575674 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=575674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let us define variables:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of adults who purchased tickets<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of children who had tickets<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250x ALIGN=MIDDLE  ALT=\"250x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount (in pesos) collected for all the adult tickets sold<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200y ALIGN=MIDDLE  ALT=\"200y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount (in pesos) collected for all the children tickets sold<BR>\n" );
document.write( "Since \"more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150 ALIGN=MIDDLE  ALT=\"150\"   DISABLED_style= \"max-width:90%; height:auto;\" > adults and children\" watched the plane, \"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E150 ALIGN=MIDDLE  ALT=\"x%2By%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since \"The sponsor of the show collected a total amount of not more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44000 ALIGN=MIDDLE  ALT=\"44000\"   DISABLED_style= \"max-width:90%; height:auto;\" > pesos\",<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250x%2B200y%3C=44000 ALIGN=MIDDLE  ALT=\"250x%2B200y%3C=44000\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "a. The mathematical statement (or statements) the represent the given situation is (or are)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E150 ALIGN=MIDDLE  ALT=\"x%2By%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" > .....eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250x%2B200y%3C=44000%29 ALIGN=MIDDLE  ALT=\"250x%2B200y%3C=44000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......eq.2<BR>\n" );
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document.write( "b. To graph an inequality, such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E150 ALIGN=MIDDLE  ALT=\"x%2By%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" > , you draw boundary lines for the region that is the solution, and color or shade the region that is the solution.<BR>\n" );
document.write( "You draw a solid line when the points on that line are part of the solution.<BR>\n" );
document.write( "You draw a dashed line when the points on that line are not part of the solution.\r<BR>\n" );
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document.write( "To determine the line you need to points.<BR>\n" );
document.write( "For example, for the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=150 ALIGN=MIDDLE  ALT=\"x%2By=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > (boundary line for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E150 ALIGN=MIDDLE  ALT=\"x%2By%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" > ),<BR>\n" );
document.write( "you can use the points (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150 ALIGN=MIDDLE  ALT=\"150\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150 ALIGN=MIDDLE  ALT=\"150\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "You get by (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150 ALIGN=MIDDLE  ALT=\"150\"   DISABLED_style= \"max-width:90%; height:auto;\" >) by choosing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2By=150 ALIGN=MIDDLE  ALT=\"0%2By=150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=150 ALIGN=MIDDLE  ALT=\"y=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You get by (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150 ALIGN=MIDDLE  ALT=\"150\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) by choosing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B0=150 ALIGN=MIDDLE  ALT=\"x%2B0=150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=150 ALIGN=MIDDLE  ALT=\"x=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "After drawing the line, you decide which side of the line is the solution.<BR>\n" );
document.write( "For example, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E150 ALIGN=MIDDLE  ALT=\"x%2By%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" > , you know that the side containing point (0,0) is not part of the solution, because<BR>\n" );
document.write( "plugging <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=0%2C+y=0%29 ALIGN=MIDDLE  ALT=\"system%28x=0%2C+y=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E150 ALIGN=MIDDLE  ALT=\"x%2By%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B0%3E150 ALIGN=MIDDLE  ALT=\"0%2B0%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > true.\r<BR>\n" );
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document.write( "On the other hand, point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=of ALIGN=MIDDLE  ALT=\"of\"   DISABLED_style= \"max-width:90%; height:auto;\" > the solution, because<BR>\n" );
document.write( "plugging <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=100 ALIGN=MIDDLE  ALT=\"x=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=100%29 ALIGN=MIDDLE  ALT=\"y=100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E150 ALIGN=MIDDLE  ALT=\"x%2By%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2B100%3E150 ALIGN=MIDDLE  ALT=\"100%2B100%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" > which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" > true.\r<BR>\n" );
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document.write( "The graph for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3E150 ALIGN=MIDDLE  ALT=\"x%2By%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be the region colored in the graph below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-50%2C200%2C-50%2C200%2C%0D%0Agrid%280%29%2C%0D%0Agraph%28300%2C300%2C-50%2C200%2C-50%2C200%2Cx%2By%3E151%29%2C%0D%0Aline%280%2C150%2C10%2C140%29%2Cline%2820%2C130%2C30%2C120%29%2C%0D%0Aline%2840%2C110%2C50%2C100%29%2Cline%2860%2C90%2C70%2C80%29%2C%0D%0Aline%2880%2C70%2C90%2C60%29%2Cline%28100%2C50%2C110%2C40%29%2C%0D%0Aline%28120%2C30%2C130%2C20%29%2Cline%28140%2C10%2C150%2C0%29%2C%0D%0Aline%28-10%2C160%2C-20%2C170%29%2Cline%28-30%2C180%2C-40%2C190%29%2C%0D%0Aline%28160%2C-10%2C170%2C-20%29%2Cline%28180%2C-30%2C190%2C-40%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The graph for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250x%2B200y%3C=44000 ALIGN=MIDDLE  ALT=\"250x%2B200y%3C=44000\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be the region colored in the graph below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-100%2C400%2C-100%2C400%2C%0D%0Agrid%280%29%2C%0D%0Agraph%28300%2C300%2C-100%2C400%2C-100%2C400%2C250x%2B200y%3C=43800%29%2C%0D%0Aline%28-100%2C345%2C256%2C-100%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For your solution, graph you want to merge the two graph.<BR>\n" );
document.write( "You also would like to show that the values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be negative,so the solution region is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=region ALIGN=MIDDLE  ALT=\"region\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inside ALIGN=MIDDLE  ALT=\"inside\"   DISABLED_style= \"max-width:90%; height:auto;\" > the quadrilateral below, plus the solid boundary lines.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C450%2C-50%2C200%2C-25%2C350%2C%0D%0Agrid%280%29%2C%0D%0Aline%280%2C220%2C176%2C0%29%2C%0D%0Aline%280%2C150%2C0%2C220%29%2Cline%28150%2C0%2C176%2C0%29%2C%0D%0Aline%280%2C150%2C10%2C140%29%2Cline%2820%2C130%2C30%2C120%29%2C%0D%0Aline%2840%2C110%2C50%2C100%29%2Cline%2860%2C90%2C70%2C80%29%2C%0D%0Aline%2880%2C70%2C90%2C60%29%2Cline%28100%2C50%2C110%2C40%29%2C%0D%0Aline%28120%2C30%2C130%2C20%29%2Cline%28140%2C10%2C150%2C0%29%2C%0D%0Ared%28circle%28100%2C95%2C3%29%29%2Clocate%28105%2C100%2CP%28100%2C95%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "c. Any point in the solution region is a solution.\r<BR>\n" );
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document.write( "For example, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100+ ALIGN=MIDDLE  ALT=\"100+\"   DISABLED_style= \"max-width:90%; height:auto;\" >adults buy tickets<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2By%3E150 ALIGN=MIDDLE  ALT=\"100%2By%3E150\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E150-50 ALIGN=MIDDLE  ALT=\"y%3E150-50\"   DISABLED_style= \"max-width:90%; height:auto;\" > means more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > children attended.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250%2A100%2B200y%3C=44000 ALIGN=MIDDLE  ALT=\"250%2A100%2B200y%3C=44000\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=95 ALIGN=MIDDLE  ALT=\"y%3C=95\"   DISABLED_style= \"max-width:90%; height:auto;\" > means no more than 95 children attended.\r<BR>\n" );
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document.write( "The point P(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=95 ALIGN=MIDDLE  ALT=\"95\"   DISABLED_style= \"max-width:90%; height:auto;\" >), meaning <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > adults and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=95 ALIGN=MIDDLE  ALT=\"95\"   DISABLED_style= \"max-width:90%; height:auto;\" > children, is on a solid boundary line and is part of the solution.\r<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );