document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151324>Question 151324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am lost with this assignment, HELP! I do not understand hwo these are answered! \r<BR>\n" );
document.write( "\n" );
document.write( "4. A group of students decides to sell pizzas to help raise money for their senior class trip. They sold pepperoni for $12, sausage for $10, and cheese for $8. At the end of their sales the class sold a total of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit.\r<BR>\n" );
document.write( "\n" );
document.write( "A. What are the three unknowns?<BR>\n" );
document.write( "	\r<BR>\n" );
document.write( "\n" );
document.write( "B. Write a separate equation representing each of the first three sentences. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "C. Determine the augmented matrix that represents the three equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "D. Solve for the matrix. Show all work to receive full credit.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "              \r<BR>\n" );
document.write( "\n" );
document.write( "E. How many of each type of pizza were sold? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111240 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=111240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
document.write( "\n" );
document.write( "Let x=# of pepperoni sold, y=# of sausage sold, and z=# of cheese sold \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)\r<BR>\n" );
document.write( "\n" );
document.write( "Since there are 3 unknowns, we need 3 equations:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Equation #1:\r<BR>\n" );
document.write( "\n" );
document.write( "First, since they sold \"pepperoni for $12, sausage for $10, and cheese for $8\" and collected $5,900, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B10y%2B8z=5900 ALIGN=MIDDLE  ALT=\"12x%2B10y%2B8z=5900\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Equation #2:\r<BR>\n" );
document.write( "\n" );
document.write( "Also, we know that the students sold 600 pizzas total. So this means that the sum of all of the pizzas sold was 600. So this translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=600 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Equation #3:\r<BR>\n" );
document.write( "\n" );
document.write( "Finally, since they sold \"175 more cheese pizzas than sausage pizzas\", this makes the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=y%2B175 ALIGN=MIDDLE  ALT=\"z=y%2B175\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Getting all of the variables to one side for equation 3 gives us: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x-y%2Bz=175 ALIGN=MIDDLE  ALT=\"0x-y%2Bz=175\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we have the system \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2812x%2B10y%2B8z=5900%2Cx%2By%2Bz=600%2C0x-y%2Bz=175%29 ALIGN=MIDDLE  ALT=\"system%2812x%2B10y%2B8z=5900%2Cx%2By%2Bz=600%2C0x-y%2Bz=175%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means that we have the augmented matrix matrix\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C12%2C10%2C8%2C5900%2C1%2C1%2C1%2C600%2C0%2C-1%2C1%2C175%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C12%2C10%2C8%2C5900%2C1%2C1%2C1%2C600%2C0%2C-1%2C1%2C175%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solution was generated by the <a  rel=nofollow HREF=\"http://www.math.odu.edu/~bogacki/lat/\">Linear Algebra Toolkit</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/augmentedmatrix.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=============================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=225 ALIGN=MIDDLE  ALT=\"x=225\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=100 ALIGN=MIDDLE  ALT=\"y=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=275 ALIGN=MIDDLE  ALT=\"z=275\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these values form the right hand column of the augmented matrix).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So this means that they sold 225 pepperoni pizzas, 100 sausage pizzas, and 275 cheese pizzas.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );