document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261713>Question 261713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A market research company finds that at a price of p=$20., they would sell x=42 tiles each month. If they lower the price to p=$10., then more people would purchase the tile, and they can expect to sell x=52 tiles in a months's time. Find the equation of the line for the demand equation. Write your answer in the form p=mx+b. Hint: write an equation using two points in the form (x,p). <BR>\n" );
document.write( "My biggest problem is I am not sure about the demand equation, I am not real clear on what I am suppose to be figuring out in this problem. I have several other problems which depend on my having this base correct. I am totally blank and have read everything I have on this and I must be over looking or thinking this out. Please help me.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192858 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=192858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> They are asking you to write your answer in the form p = m*x + b.\r<BR>\n" );
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document.write( "If I take that literally, then at a price of 20, the equation would become:\r<BR>\n" );
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document.write( "20 = m*x + b\r<BR>\n" );
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document.write( "this kind of says that the price per tile is a function of the number of tiles sold per month which doesn't make a hell of a lot of sense, because it usually is that the number of tiles sold per month is a function of the price per tile.\r<BR>\n" );
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document.write( "I would think the formula should be:\r<BR>\n" );
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document.write( "42 = m*x + b where x is the cost per tile.\r<BR>\n" );
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document.write( "you would then get:\r<BR>\n" );
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document.write( "42 = m*20 + b, and you would also get:\r<BR>\n" );
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document.write( "52 = m*10 + b.\r<BR>\n" );
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document.write( "now the number of tiles sold per month is dependent on the price per tile which I believe is what you are looking for.\r<BR>\n" );
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document.write( "I can see why you are confused.\r<BR>\n" );
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document.write( "I am too.\r<BR>\n" );
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document.write( "If you are looking at a demand equation, then you want to find the demand based on the price.\r<BR>\n" );
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document.write( "I will assume my interpretation is correct and work it that way and see where it goes.\r<BR>\n" );
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document.write( "let's assume, the equation is:\r<BR>\n" );
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document.write( "d = m*p + b\r<BR>\n" );
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document.write( "this means demand = slope of the line times the price per unit + b, where b is the demand if the price is 0.\r<BR>\n" );
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document.write( "That doesn't make a hell of a lot of sense, but these straight line equations are usually only valid in a limited range of the domain so we can use it even if there are logical consistencies involved at the extremes.\r<BR>\n" );
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document.write( "our equation is:\r<BR>\n" );
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document.write( "d = m*p + b\r<BR>\n" );
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document.write( "our coordinate points are:\r<BR>\n" );
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document.write( "(p1,d1) = (20,42)<BR>\n" );
document.write( "(p2,d2) = (10,52)\r<BR>\n" );
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document.write( "we find the slope (m) by the formula (d2-d1)/(p2-p1) = (52-42)/(10-20) = 10/-10 = -1.\r<BR>\n" );
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document.write( "our equation becomes:\r<BR>\n" );
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document.write( "d = -1*p + b\r<BR>\n" );
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document.write( "we substitute one of the points on the line to find b.\r<BR>\n" );
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document.write( "take (p2,d2) = (10,52)\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "52 = -1*10 + b which becomes 52 = -10 + b which becomes 62 = b after you add 10 to both sides of that equation.\r<BR>\n" );
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document.write( "our equation becomes:\r<BR>\n" );
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document.write( "d = -p + 62\r<BR>\n" );
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document.write( "when p = 0, then d = 62<BR>\n" );
document.write( "when p = 10, then d = 52<BR>\n" );
document.write( "when p = 20, then d = 42\r<BR>\n" );
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document.write( "we let y = d and x = p so we can graph this equation.\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "y = -x + 62\r<BR>\n" );
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document.write( "graph of the equation is shown below:\r<BR>\n" );
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document.write( "this is your demand equation.\r<BR>\n" );
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document.write( "it is estimating the demand based on the price.\r<BR>\n" );
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document.write( "y values are the demand.\r<BR>\n" );
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document.write( "x values are the price.\r<BR>\n" );
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document.write( "as the price goes up, the demand goes down.\r<BR>\n" );
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document.write( "as the price goes down, the demand goes up.\r<BR>\n" );
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document.write( "they threw you a curve when they said use the equation in the form of p = m*x+b and when they showed you that p = 20.\r<BR>\n" );
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document.write( "this means that p is the price per unit and the equation is not a demand equation but a price equation which is making the price dependent on the demand rather than the demand dependent on the price.\r<BR>\n" );
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document.write( "I think that what you are looking for is the demand equation which means that the demand is dependent on the price, so the equation I gave you is accurate.\r<BR>\n" );
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document.write( "If the price were dependent on the demand, then that would be a price equation which is not what I think you are looking for.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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