document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885582>Question 885582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question 4: (1 point)\r<BR>\n" );
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document.write( "At a tennis club, a 15,000 ft2 rectangular area is partitioned into three rectangular courts of equal size. A total of 800 feet of fencing is used to enclose the three courts, including the interior sides.\r<BR>\n" );
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document.write( "Maple plot\r<BR>\n" );
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document.write( "What are the possible dimensions, in feet, of the entire rectangular area?\r<BR>\n" );
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document.write( "Select all that apply.\r<BR>\n" );
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document.write( " (a) <BR>\n" );
document.write( "25feet by 600feet<BR>\n" );
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document.write( " (b) <BR>\n" );
document.write( "100feet by 150feet<BR>\n" );
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document.write( " (c) <BR>\n" );
document.write( "100feet by 300feet<BR>\n" );
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document.write( " (d) <BR>\n" );
document.write( "300feet by 50feet<BR>\n" );
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document.write( " (e) <BR>\n" );
document.write( "100feet by 50feet<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535316 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=535316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The answer they want is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28d%29%29 ALIGN=MIDDLE  ALT=\"highlight%28%28d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "I would answer that and try hard not to say more.<BR>\n" );
document.write( "Answer (b) Is also mathematically correct, and looks like a possibility for people not familiar with tennis.<BR>\n" );
document.write( "That makes the question culturally biased, and makes the designer of the question look incompetent at math.<BR>\n" );
document.write( "However, pointing out that may not gain you any points.<BR>\n" );
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document.write( "MULTIPLE CHOICE STRATEGY:<BR>\n" );
document.write( "Think efficiently, and do not waste time thinking too much and/or writing too many equations.\r<BR>\n" );
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document.write( "You can use the area information to quickly rule out (c) and (e):<BR>\n" );
document.write( "The area for (c) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100feet%29%2A%28300feet%29=%2230%2C000%22 ALIGN=MIDDLE  ALT=\"%28100feet%29%2A%28300feet%29=%2230%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ft%5E2 ALIGN=MIDDLE  ALT=\"ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "the area for (e) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100feet%29%2A%2850feet%29=%225%2C000%22 ALIGN=MIDDLE  ALT=\"%28100feet%29%2A%2850feet%29=%225%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ft%5E2 ALIGN=MIDDLE  ALT=\"ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Neither one of those is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2215%2C000%22 ALIGN=MIDDLE  ALT=\"%2215%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ft%5E2 ALIGN=MIDDLE  ALT=\"ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so (c) and (e) are not solutions.<BR>\n" );
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document.write( "\"Make plot\" means draw a quick sketch.<BR>\n" );
document.write( "It does not need to be a good drawing, and it cannot be to scale since you do not know the answer yet.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C100%2C-1%2C36%2C-3%2C9%2C%0D%0Ared%28rectangle%280%2C0%2C30%2C8%29%29%2C%0D%0Ared%28rectangle%2810%2C0%2C20%2C8%29%29%2C%0D%0Alocate%2812%2C0%2Clength%29%2Clocate%2830.5%2C5%2Cwidth%29%2C%0D%0Aarrow%2811%2C-1%2C0%2C-1%29%2Carrow%2819%2C-1%2C30%2C-1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The red lines represent the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800 ALIGN=MIDDLE  ALT=\"800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=feet ALIGN=MIDDLE  ALT=\"feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > of fencing, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Alength%2B4%2Awidth=800feet ALIGN=MIDDLE  ALT=\"2%2Alength%2B4%2Awidth=800feet\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=length%2B2width=400feet ALIGN=MIDDLE  ALT=\"length%2B2width=400feet\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "How do choices (a), (b), and (d), fare against that requirement? <BR>\n" );
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document.write( "For (a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A25feet%2B600feet=50feet%2B600feet=650feet ALIGN=MIDDLE  ALT=\"2%2A25feet%2B600feet=50feet%2B600feet=650feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so (a) does not work.<BR>\n" );
document.write( "You did not even need to calculate because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600feet ALIGN=MIDDLE  ALT=\"600feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > length is by itself more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400feet ALIGN=MIDDLE  ALT=\"400feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "For (d) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A50feet%2B300feet=100feet%2B300feet=400feet ALIGN=MIDDLE  ALT=\"2%2A50feet%2B300feet=100feet%2B300feet=400feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28d%29%29 ALIGN=MIDDLE  ALT=\"highlight%28%28d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a solution.<BR>\n" );
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document.write( "Since the problem is worth just one point, you do not need to think too long about it.<BR>\n" );
document.write( "If all the choices are single answers,<BR>\n" );
document.write( "as soon as you get an answer that everyone would like,<BR>\n" );
document.write( "even if you have not tried the other options,<BR>\n" );
document.write( "you choose that answer, and move on to another question.<BR>\n" );
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document.write( "THINKING TOO MUCH:<BR>\n" );
document.write( "For (b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A100feet%2B150feet=200feet%2B150feet=350feet ALIGN=MIDDLE  ALT=\"2%2A100feet%2B150feet=200feet%2B150feet=350feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > , does not work.<BR>\n" );
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document.write( "However, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A150feet%2B100feet=300feet%2B100feet=400feet ALIGN=MIDDLE  ALT=\"2%2A150feet%2B100feet=300feet%2B100feet=400feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > works, so (b) 100feet by 150feet could be a solution, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=length=100feet ALIGN=MIDDLE  ALT=\"length=100feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=width=150 ALIGN=MIDDLE  ALT=\"width=150\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "In the plot/sketch, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=length ALIGN=MIDDLE  ALT=\"length\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=width ALIGN=MIDDLE  ALT=\"width\"   DISABLED_style= \"max-width:90%; height:auto;\" > were just variable names representing the measurements of the two sides of the big rectangle.<BR>\n" );
document.write( "It is not necessary that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=length%3Ewidth ALIGN=MIDDLE  ALT=\"length%3Ewidth\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=length ALIGN=MIDDLE  ALT=\"length\"   DISABLED_style= \"max-width:90%; height:auto;\" > meant the longer side of that rectangular <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2215%2C000%22 ALIGN=MIDDLE  ALT=\"%2215%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ft%5E2 ALIGN=MIDDLE  ALT=\"ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > area.<BR>\n" );
document.write( "I bet the people who designed the question never thought of that.<BR>\n" );
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document.write( "Answer (b) 100feet by 150feet is mathematically correct.<BR>\n" );
document.write( "Unfortunately, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=length=100feet ALIGN=MIDDLE  ALT=\"length=100feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=width=150 ALIGN=MIDDLE  ALT=\"width=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > would mean that each court would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33%261%2F3 ALIGN=MIDDLE  ALT=\"33%261%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ft ALIGN=MIDDLE  ALT=\"ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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=ft ALIGN=MIDDLE  ALT=\"ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and that is too narrow and too long for a tennis court. (I looked it up).<BR>\n" );
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document.write( "WRITING TOO MANY EQUATIONS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" >= one of the dimensions of the total area to be fenced, in feet.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W ALIGN=MIDDLE  ALT=\"W\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the other dimension of the total area to be fenced, in feet.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2AW=15000 ALIGN=MIDDLE  ALT=\"L%2AW=15000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=15000%2FL ALIGN=MIDDLE  ALT=\"W=15000%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" > (because the area is 15,000 square feet).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2B4W=800 ALIGN=MIDDLE  ALT=\"2L%2B4W=800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2B2W=400 ALIGN=MIDDLE  ALT=\"L%2B2W=400\"   DISABLED_style= \"max-width:90%; height:auto;\" > (because 800ft is total amount of fence, and the sketch/plot shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2B4W ALIGN=MIDDLE  ALT=\"2L%2B4W\"   DISABLED_style= \"max-width:90%; height:auto;\" > is that length as a function of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W ALIGN=MIDDLE  ALT=\"W\"   DISABLED_style= \"max-width:90%; height:auto;\" > ).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28L%2B2W=400%2CW=15000%2FL%29 ALIGN=MIDDLE  ALT=\"system%28L%2B2W=400%2CW=15000%2FL%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2B2%2815000%2FL%29=400 ALIGN=MIDDLE  ALT=\"L%2B2%2815000%2FL%29=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2B30000%2FL=400 ALIGN=MIDDLE  ALT=\"L%2B30000%2FL=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2B30000L=400L ALIGN=MIDDLE  ALT=\"L%5E2%2B30000L=400L\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2-400L%2B30000=0 ALIGN=MIDDLE  ALT=\"L%5E2-400L%2B30000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Any way you solve that equation, you get two solutions:<BR>\n" );
document.write( "either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=300 ALIGN=MIDDLE  ALT=\"L=300\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=15000%2F300 ALIGN=MIDDLE  ALT=\"W=15000%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=50 ALIGN=MIDDLE  ALT=\"W=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=100 ALIGN=MIDDLE  ALT=\"L=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=15000%2F100 ALIGN=MIDDLE  ALT=\"W=15000%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=150 ALIGN=MIDDLE  ALT=\"W=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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