document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138848>Question 1138848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person was in charge of ordering 26 pizzas for the office party. He ordered three types of​ pizza: cheese,​ pepperoni, and supreme. The cheese pizzas cost $6 ​each, the pepperoni pizzas cost $9 ​each, and the supreme pizzas cost $12 each. He spent exactly twice as much on the pepperoni pizzas as he did on the cheese pizzas. If the person spent a total of $222 on​ pizza, how many pizzas of each type did he​ buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756631 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "c = # of cheese pizzas<BR>\n" );
document.write( "p = # of pepperoni pizzas<BR>\n" );
document.write( "s = # of supreme pizzas<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Bp%2Bs+=+26 ALIGN=MIDDLE  ALT=\"c%2Bp%2Bs+=+26\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the total number of pizzas was 26<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%2B9p%2B12s+=+222 ALIGN=MIDDLE  ALT=\"6c%2B9p%2B12s+=+222\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the total cost was $222<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9p+=+2%286c%29 ALIGN=MIDDLE  ALT=\"9p+=+2%286c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the cost of the pepperoni pizzas was twice the cost of the cheese pizzas<br><BR>\n" );
document.write( "There is an endless number of different paths for solving that system of 3 equations in 3 variables.  The path I chose involved many twists and turns and was not particularly pleasant....<br><BR>\n" );
document.write( "So instead of finishing the problem that way, let's spend a little effort to set up the problem using a single equation in a single variable and see if the resulting path to the solution is easier.<br><BR>\n" );
document.write( "He spent twice as much on the $9 pepperoni pizzas as he spent on the $6 cheese pizzas:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9p+=+2%286c%29 ALIGN=MIDDLE  ALT=\"9p+=+2%286c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9p+=+12c ALIGN=MIDDLE  ALT=\"9p+=+12c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3p+=+4c ALIGN=MIDDLE  ALT=\"3p+=+4c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Using this, we can let p=4x and c=3x; then 3p=4c=12x.<br><BR>\n" );
document.write( "And then with p=4x and c=3x, and with 26 pizzas in all, the number of supreme pizzas is 26-7x.<br><BR>\n" );
document.write( "Then...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%283x%29%2B9%284x%29%2B12%2826-7x%29+=+222 ALIGN=MIDDLE  ALT=\"6%283x%29%2B9%284x%29%2B12%2826-7x%29+=+222\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%2B36x%2B312-84x+=+222 ALIGN=MIDDLE  ALT=\"18x%2B36x%2B312-84x+=+222\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-30x%2B312+=+222 ALIGN=MIDDLE  ALT=\"-30x%2B312+=+222\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90+=+30x ALIGN=MIDDLE  ALT=\"90+=+30x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "cheese: 3x = 9<BR>\n" );
document.write( "pepperoni: 4x = 12<BR>\n" );
document.write( "supreme: 26-7x = 5<br><BR>\n" );
document.write( "With the two ways I chose to solve the problem, the little extra effort required to set up an equation using a single variable resulted in an equation that required far less effort to solve than the system of 3 equations in 3 variables.<br><BR>\n" );
document.write( "While it is of course important to understand how to set up a problem like this with 3 variables directly from the given information, it is also important to know that very often the overall effort required to solve a problem will be greatly reduced if you can set up the problem using a single variable. </SPAN>\n" );
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