document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=662256>Question 662256</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im trying to help my sister with her hw yet i dont kno how to do this, would someone help me so i could teach her<BR>\n" );
document.write( "Milk Problem: Handy Andy sells one-gallon cartons of milk (4 quarts) for $3.09 each and half-gallon cartons for $1.65 each. Assume that the number of cents you pay for a carton of milk varies linearly with the number of quarts the carton holds. <BR>\n" );
document.write( "a) Write the particular equation expressing price in terms of quarts.<BR>\n" );
document.write( "b) If Handy Andy sold 3-gallon cartons, what would your equation predict the price to be?<BR>\n" );
document.write( "c) The actual prices for pint cartons (1/2 quart) and one-quart cartons are $.57 and $.99, respectively. Do these prices fit your mathematical model? If not, are they higher than predicted or lower?<BR>\n" );
document.write( "d) Suppose that you found cartons of milk marked at $3.45, but that there was nothing on the carton to tell what size it is. According to your model, how much would such a carton hold?<BR>\n" );
document.write( "e) What doe the price-intercept represent in the real world?<BR>\n" );
document.write( "f) What are the units of the slope? What real-world quantity does this number represent?<BR>\n" );
document.write( "g) Sketch and label the graph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412350 by </B><A HREF=/tutors/aboutme.mpl?userid=mari_hernandez><B>mari_hernandez(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mari_hernandez><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=412350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  = number of quarts<BR>\n" );
document.write( " = price in $\r<BR>\n" );
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document.write( "(Explanation: We have to start by defining variables that will be related by a linear equation. Next, we have to use the two (x,y) data points given to find the equation)\r<BR>\n" );
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document.write( "one gallon (4 quarts) for $3.09 --> (4,3.09) (x=4, y=3.09)<BR>\n" );
document.write( "half gallon (2 quarts) for $1.65 --> (2,1.65) (x=2, y=1.65)\r<BR>\n" );
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document.write( "a) Write the particular equation expressing price in terms of quarts.<BR>\n" );
document.write( "(Explanation: We are looking for an equation of the form . We can substitute the (x,y) values for each data point to get a system of equation to solve for  and . Otherwise, we can use the two points to calculate the slope  of the line, and then we can find the rest of the equation one way or another) <BR>\n" );
document.write( "Using a system of equations:\r<BR>\n" );
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document.write( "Subtracting the second equation from the first equation;\r<BR>\n" );
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document.write( "-<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( " -->  --> <BR>\n" );
document.write( "Substituting that value in the second equation, we get<BR>\n" );
document.write( " -->  -->  --> <BR>\n" );
document.write( "The equation is  <BR>\n" );
document.write( "Using slope:<BR>\n" );
document.write( "(Explanation: the slope,  in the change in y divided by the change in x, as we go from one data point to the other.)<BR>\n" );
document.write( " -->  --> <BR>\n" );
document.write( "The point-slope form of the equation, using point (2,1.65), is:\r<BR>\n" );
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document.write( " -->  -->  --> \r<BR>\n" );
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document.write( "b) If Handy Andy sold 3-gallon cartons, what would your equation predict the price to be?\r<BR>\n" );
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document.write( "Substituting  in the equation, we get<BR>\n" );
document.write( " -->  --> <BR>\n" );
document.write( "Andy would sell a 3-gallon carton for $8.85. \r<BR>\n" );
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document.write( "c) The actual prices for pint cartons (1/2 quart) and one-quart cartons are $.57 and $.99, respectively. Do these prices fit your mathematical model? If not, are they higher than predicted or lower?<BR>\n" );
document.write( "The predictions are found using the equation <BR>\n" );
document.write( "For 1/2 quart =  quart, , so<BR>\n" );
document.write( " -->  --> <BR>\n" );
document.write( "For 1 quart, , so<BR>\n" );
document.write( " -->  --> <BR>\n" );
document.write( "the price for pint cartons agrees with the  prediction,<BR>\n" );
document.write( "but the price for the quart, $0.99, is higher than the  prediction.\r<BR>\n" );
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document.write( "d)<BR>\n" );
document.write( "I would use  and the equation  to find the number of quarts, .\r<BR>\n" );
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document.write( " a carton would hold 4.5 quarts according to the model.\r<BR>\n" );
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document.write( "e)<BR>\n" );
document.write( "The price-intercept is the y-intercept in the equation .<BR>\n" );
document.write( "It is the value, , representing $0.21, the price of a carton with zero quarts of milk inside. It represents the cost of the carton plus maybe Andy's work making a sale.\r<BR>\n" );
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document.write( "f) What are the units of the slope? What real-world quantity does this number represent?<BR>\n" );
document.write( "The slope, , represents the cost of the milk per quart.<BR>\n" );
document.write( "The units are $/quart, and it gets multiplied by the number of quarts to find the price of the milk inside the carton in $. <BR>\n" );
document.write( " </SPAN>\n" );
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