document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029850>Question 1029850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plain hamburger requires one ground beef patty and a bun. A cheeseburger requires one ground beef patty, one slice of cheese, and a bun. A double cheeseburger requires two ground beef patties, two slices of cheese, and a bun. \r<BR>\n" );
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document.write( " Frozen hamburger patties are typically sold in packs of 12; hamburger buns, in packs of 8; and cheese slices, in packs of 24. \r<BR>\n" );
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document.write( " A family is in charge of providing burgers for a neighborhood block party. They have purchased 14 packs of buns, 12 packs of hamburger patties, and 3 packs of cheese slices. How many of each type of sandwich should they make if they want to use up all of the buns, patties, and cheese slices?\r<BR>\n" );
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document.write( "plain hamburgers  _____      <BR>\n" );
document.write( "cheeseburgers ______       <BR>\n" );
document.write( "double cheeseburgers ______<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 #644903 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We start by giving variable names that will work as placeholders for the values we need to find:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of plain burgers,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of cheeseburgers,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of double cheeseburgers.<BR>\n" );
document.write( "(Some people like to use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "but I like variable names that remind of their meaning).<BR>\n" );
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document.write( "All the burgers require <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > bun per burger,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bc%2Bd ALIGN=MIDDLE  ALT=\"p%2Bc%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > buns are needed,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2A8 ALIGN=MIDDLE  ALT=\"14%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" > buns are available(14 packs of 8 buns per pack).<BR>\n" );
document.write( "That gives us the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bc%2Bd=14%2A8 ALIGN=MIDDLE  ALT=\"p%2Bc%2Bd=14%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bc%2Bd=112 ALIGN=MIDDLE  ALT=\"p%2Bc%2Bd=112\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "The plain burgers, and the cheeseburgers require one patty each,<BR>\n" );
document.write( "but each double cheeseburger required 2 patties,<BR>\n" );
document.write( "so the number of frozen hamburger patties required is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bc%2B2d ALIGN=MIDDLE  ALT=\"p%2Bc%2B2d\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2A12 ALIGN=MIDDLE  ALT=\"12%2A12\"   DISABLED_style= \"max-width:90%; height:auto;\" > patties area available (12 packs, with 12 frozen hamburger patties per pack).<BR>\n" );
document.write( "That gives us the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bc%2B2d=12%2A12 ALIGN=MIDDLE  ALT=\"p%2Bc%2B2d=12%2A12\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bc%2B2d=144 ALIGN=MIDDLE  ALT=\"p%2Bc%2B2d=144\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "A plain hamburger requires no cheese,<BR>\n" );
document.write( "while a cheeseburger requires one slice of cheese,<BR>\n" );
document.write( "and a double cheeseburger required 2 slices,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B2d ALIGN=MIDDLE  ALT=\"c%2B2d\"   DISABLED_style= \"max-width:90%; height:auto;\" > slices of cheese will be needed.<BR>\n" );
document.write( "There area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A24 ALIGN=MIDDLE  ALT=\"3%2A24\"   DISABLED_style= \"max-width:90%; height:auto;\" > slices of cheese available (3 packs, with 24 slices per pack),<BR>\n" );
document.write( "and that gives us the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B2d=3%2A24 ALIGN=MIDDLE  ALT=\"c%2B2d=3%2A24\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B2d=72 ALIGN=MIDDLE  ALT=\"c%2B2d=72\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "The three equation form the easy system of linear equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28p%2Bc%2Bd=112%2Cp%2Bc%2B2d=144%2Cc%2B2d=72%29 ALIGN=MIDDLE  ALT=\"system%28p%2Bc%2Bd=112%2Cp%2Bc%2B2d=144%2Cc%2B2d=72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Subtracting the first equation from the second, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=32%29 ALIGN=MIDDLE  ALT=\"highlight%28d=32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substituting that value in the third equation we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B2%2A32=72 ALIGN=MIDDLE  ALT=\"c%2B2%2A32=72\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B64=72 ALIGN=MIDDLE  ALT=\"c%2B64=72\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=72-64 ALIGN=MIDDLE  ALT=\"c=72-64\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=8%29 ALIGN=MIDDLE  ALT=\"highlight%28c=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Substituting the values found for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B8%2B32=112 ALIGN=MIDDLE  ALT=\"p%2B8%2B32=112\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B40=112 ALIGN=MIDDLE  ALT=\"p%2B40=112\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=112-40 ALIGN=MIDDLE  ALT=\"p=112-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=72%29 ALIGN=MIDDLE  ALT=\"highlight%28p=72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "plain hamburgers  72 <BR>\n" );
document.write( "cheeseburgers  8 <BR>\n" );
document.write( "double cheeseburgers  32. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );