document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=908>Question 908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A restaurant charges $3.50 for its “all you can eat” breakfast buffet, and $5.00 for its lunch buffet. At 2 PM<BR>\n" );
document.write( "the manager found that 100 people had eaten in the restaurant that day, and the total receipts were $428.How many people had eaten breakfast and how many had eaten lunch? Solve this problem using any method, however to receive full credit, you must specify which method you are using and show supporting<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #301 by </B><A HREF=/tutors/aboutme.mpl?userid=matwiz><B>matwiz(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=matwiz><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=301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let X be the people who ate breakfast, Y be the people who ate lunch<BR>\n" );
document.write( "We know that<BR>\n" );
document.write( "(a) x + y = 100\r<BR>\n" );
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document.write( "and that \r<BR>\n" );
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document.write( "(b) 3.50x + 5.00y = 428\r<BR>\n" );
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document.write( "for (a), I choose to rewrite it as y = 100-x\r<BR>\n" );
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document.write( "Thence we have for (b):\r<BR>\n" );
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document.write( "3.50x + 5.00(100 - x) = 428<BR>\n" );
document.write( "3.5x + 500 - 5x = 428\r<BR>\n" );
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document.write( "-1.5x = - 72<BR>\n" );
document.write( "x = 48 ate breakfast\r<BR>\n" );
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document.write( "y = 100 - 48 = 52 ate lunch\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "$3.50 x 48 + $5.00 x 52 = $168 + $260 = $428\r<BR>\n" );
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document.write( "The solution checks\r<BR>\n" );
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document.write( " </SPAN>\n" );
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