document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190631>Question 190631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of students decides to sell pizzas to help raise money.  They sold pepperoni for $12, sausage for $10, and cheese for $8.  The class sold a total of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage.  Set up a system of three equations and three unkowns, use the augemented matrix to solve. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143113 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=143113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let \r<BR>\n" );
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document.write( "x = # of pepperoni pizzas sold\r<BR>\n" );
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document.write( "y = # of sausage pizzas sold\r<BR>\n" );
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document.write( "z = # of cheese pizzas sold\r<BR>\n" );
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document.write( "First, translate the sentences to get the following system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By%2Bz=600%2C12x%2B10y%2B8z=5900%2Cz=y%2B175%29 ALIGN=MIDDLE  ALT=\"system%28x%2By%2Bz=600%2C12x%2B10y%2B8z=5900%2Cz=y%2B175%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, transfer the coefficients and the constants to form the augmented matrix:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C1%2C1%2C1%2C600%2C12%2C10%2C8%2C5900%2C0%2C-1%2C1%2C175%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C1%2C1%2C1%2C600%2C12%2C10%2C8%2C5900%2C0%2C-1%2C1%2C175%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's perform the row reduction to solve for x, y, and z (rref steps provided by <a  rel=nofollow HREF=\"http://www.math.odu.edu/~bogacki/lat/\">The Linear Algebra Toolkit</a>):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/rref2.png\">\r<BR>\n" );
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document.write( "Since the last column has the values 225, 100, and 275, this means that <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;\" >\r<BR>\n" );
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document.write( "So the students sold 225 pepperoni pizzas, 100 sausage pizzas, and 275 cheese pizzas.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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