document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194481>Question 1194481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a price of $10.96 per pound, the supply of beef ribeye is 354 thousand pounds and the demand is 405 thousand pounds. At a price of $12.52, the supply of beef ribeye is 415 thousand pounds and the demand is 344 thousand pounds.\r<BR>\n" );
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document.write( "(a) Find a price-supply equation of the form p=mx+b, where x is the quantity in thousands of pounds. Since one side of the equation has already been provided, you may provide your answer below is a constant times x plus a constant, or any algebraically equivalent expression.<BR>\n" );
document.write( "p= <BR>\n" );
document.write( "(b) Find a price-demand equation of the form p=mx+b, where x is the quantity in thousands of pounds.<BR>\n" );
document.write( "p= <BR>\n" );
document.write( "(c) What is the equilibrium quantity?<BR>\n" );
document.write( " thousand pounds\r<BR>\n" );
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document.write( "(d) What is the equilibrium price? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826701 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=826701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you let x = the number of pounds of beef and y = the price per pound of beef, then you get the following points in (x,y) format.<BR>\n" );
document.write( "supply points are (354000,10.96) and (415000,12.52)<BR>\n" );
document.write( "demand points are (405000,10.96) and (344,000,12.52)\r<BR>\n" );
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document.write( "the linear equation is in the form of y = mx + b<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "the slope in each equation is (y2-y1) / (x2-x1)\r<BR>\n" );
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document.write( "for the demand equation, the slope becomes (12.52 - 10.96) / (344000 - 405000) which is equal to 1.56 / -61000 which can be shown as -1.56/61000.\r<BR>\n" );
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document.write( "for the supply equation, the slope becomes (12.52 - 10.96) / (415000 - 354000) which is equal to 1.56 / 61000 which can be shown as 1.56/61000.\r<BR>\n" );
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document.write( "the demand equation becomes y = -1.56/61000 + b<BR>\n" );
document.write( "the supply equation becomes y = 1.56/61000 + b\r<BR>\n" );
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document.write( "to solve for b in each equation, take one of the points in each equation and use that point to find b.\r<BR>\n" );
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document.write( "in the demand equation, y  = -1.56/61000 * x + b becomes 10.96 = -1.56/61000 * 405000 + b.<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = 10.96 + 1.56/61000*405000 = 21.31737705.\r<BR>\n" );
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document.write( "in the supply equation, y = 1.56/61000 * x + b becomes 10.96 = 1.56/61000 * 354000 + b.<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = 10.96 - 1.56/61000 * 354000 = 1.906885246.\r<BR>\n" );
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document.write( "your demand equation becomes y = -1.56/61000 * x + 21.31737705.<BR>\n" );
document.write( "your supply equation becomes y = 1.56/61000 * x + 1.906885246.\r<BR>\n" );
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document.write( "in these equations, x represents the number of pounds of beef and y represents the price per pound.\r<BR>\n" );
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document.write( "y and p are interchangeable, since they both represent the same thing.<BR>\n" );
document.write( "using p, you get:<BR>\n" );
document.write( "your demand equation becomes p = -1.56/61000 * x + 21.31737705.<BR>\n" );
document.write( "your supply equation becomes p = 1.56/61000 * x + 1.906885246.<BR>\n" );
document.write( "y replaces p for graphing purposes only.\r<BR>\n" );
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document.write( "the equilibrium point is when the demand is equal to the supply.<BR>\n" );
document.write( "this occurs when the pounds of beef are the same for the supply and for the demand.<BR>\n" );
document.write( "to find that point, set the equations equal to each other and solve for x.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "-1.56/61000 * x + 21.31737705 = 1.56/61000 * x + 1.906885246.<BR>\n" );
document.write( "add 1.56/61000 to both sides of the equation and subtract 1.906885246 from both sides of the equation to get:<BR>\n" );
document.write( "3.12/61000 * x = 19.4104918<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 19.4104918 * 61000 / 3.12 = 379500.\r<BR>\n" );
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document.write( "the supply and demand will be in equilibrium when 379,500 pounds of beef are supplied and demanded.\r<BR>\n" );
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document.write( "when that happens, the price per pound of beef will be equal to 11.61213115.\r<BR>\n" );
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document.write( "i graphed both equations.<BR>\n" );
document.write( "red is the demand equation.<BR>\n" );
document.write( "blue is the supply equation.<BR>\n" );
document.write( "the graph looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/052503.jpg\" >\r<BR>\n" );
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document.write( "answers to your questions are shown below.\r<BR>\n" );
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document.write( "(a) Find a price-supply equation of the form p=mx+b, where x is the quantity in thousands of pounds. Since one side of the equation has already been provided, you may provide your answer below is a constant times x plus a constant, or any algebraically equivalent expression.<BR>\n" );
document.write( "p = 1.56/61000 * x + 1.906885246\r<BR>\n" );
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document.write( "(b) Find a price-demand equation of the form p=mx+b, where x is the quantity in thousands of pounds.<BR>\n" );
document.write( "p = -1.56/61000 * x + 21.31737705.\r<BR>\n" );
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document.write( "(c) What is the equilibrium quantity?<BR>\n" );
document.write( "379.5 thousand pounds (379,500).\r<BR>\n" );
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document.write( "(d) What is the equilibrium price?<BR>\n" );
document.write( "11.61213115 dollars per pound.\r<BR>\n" );
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document.write( "let me know is you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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