document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=180879>Question 180879</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780618851881/algebrahomeworkh>College Algebra a Graphing Approach</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Rental Demand:A real estate office handles an apartment complex with 50 units. When the rent per unit is $580 per month, all 50 units are occupied. However, when the rent is $625 per month, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear.\r<BR>\n" );
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document.write( "a. Write the equation of the line giving the demand x in terms of the rent p.\r<BR>\n" );
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document.write( "b. Use a graphing utility to graph the demand equation and use the trace feature to estimate the number of units occupied when the reant is $655. Verify your answer algebraically.\r<BR>\n" );
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document.write( "c. Use teh demand equation to predict the number of units occupied when the rent is lowered to $595. Verify your answer graphically.\r<BR>\n" );
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document.write( "Thanks - I'm so frustrated and have been stuck on word problems for 2 weeks. - Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #135621 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=135621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A real estate office handles an apartment complex with 50 units. When the rent<BR>\n" );
document.write( " per unit is $580 per month, all 50 units are occupied. However, when the rent<BR>\n" );
document.write( " is $625 per month, the average number of occupied units drops to 47.<BR>\n" );
document.write( " Assume that the relationship between the monthly rent p and the demand x is linear.<BR>\n" );
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document.write( "a. Write the equation of the line giving the demand x in terms of the rent p.<BR>\n" );
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document.write( "Using the slope formula: m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > find the slope<BR>\n" );
document.write( "Assign the given values as follows<BR>\n" );
document.write( "x1 = 580; y1 = 50<BR>\n" );
document.write( "x2 = 625; y2 = 47<BR>\n" );
document.write( "m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2847-50%29%2F%28625-580%29 ALIGN=MIDDLE  ALT=\"%2847-50%29%2F%28625-580%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2F%2845%29 ALIGN=MIDDLE  ALT=\"%28-3%29%2F%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F15 ALIGN=MIDDLE  ALT=\"-1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Write the equation using the point/slope formula y - y1 = m(x - x1)<BR>\n" );
document.write( "y - 50 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F15 ALIGN=MIDDLE  ALT=\"-1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x - 580)<BR>\n" );
document.write( "y - 50 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F15 ALIGN=MIDDLE  ALT=\"-1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x - 580)<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F15 ALIGN=MIDDLE  ALT=\"-1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 38.67 + 50<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F15 ALIGN=MIDDLE  ALT=\"-1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 88.67<BR>\n" );
document.write( "The way they have written it, demand (d) dependent on price (p) it would be<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F15 ALIGN=MIDDLE  ALT=\"-1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >p + 88.67<BR>\n" );
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document.write( "b. Use a graphing utility to graph the demand equation and use the trace feature to estimate the number of units occupied when the rent is $655. Verify your answer algebraically.<BR>\n" );
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document.write( "Substitute 655 for p in the above equation<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F15%29 ALIGN=MIDDLE  ALT=\"%28-1%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >(655) + 88.67<BR>\n" );
document.write( "d = -43.67 + 88.67<BR>\n" );
document.write( "d = 45 units rented at $655<BR>\n" );
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document.write( " On a TI83, it would look something like this:<BR>\n" );
document.write( "(Xmin=-100, Xmax=800; Ymin=-20, Ymax=100)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-100%2C+800%2C+-20%2C+100%2C+%28-1%2F15%29x%2B88.67%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-100%2C+800%2C+-20%2C+100%2C+%28-1%2F15%29x%2B88.67%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "c. Use the demand equation to predict the number of units occupied when the rent is lowered to $595. Verify your answer graphically.<BR>\n" );
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document.write( "Substitute 595 for p in the above equation in the same way<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F15%29 ALIGN=MIDDLE  ALT=\"%28-1%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >(595) + 88.67<BR>\n" );
document.write( "d = -39.67 + 88.67<BR>\n" );
document.write( "d = 49 units rented at $595, verify on the same graph<BR>\n" );
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document.write( "they should not have assigned the demand as x. x is usually the independent<BR>\n" );
document.write( "variable and here, the demand is the dependent variable. Causes confusion.<BR>\n" );
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document.write( "Hopefully, this has relieved some of your frustration, and you can enjoy the rest of this blessed Sunday!  Carl </SPAN>\n" );
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