document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127524>Question 1127524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Adrian, Nathan, and Brian bought lunch from the concession stand. Adrian paid $5.50 for burgers, fries and a drink; Nathan paid $4.00 for a burger and a drink; and Brian paid $4.25 for a burger and fries.<BR>\n" );
document.write( "a) write three equations modeling the cost of their lunches using b, f, and d to represent the cost of a burger, fries, and a drink.<BR>\n" );
document.write( "b)solve the system of equations to determine the cost of each food item.<BR>\n" );
document.write( "i just need help setting it up </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743939 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let burgers be x, fries y, and drink z<BR>\n" );
document.write( "solving by elimination:<BR>\n" );
document.write( "x + y + z = 5.50 = 11/2 multiply all times 2 to get rid of the fraction<BR>\n" );
document.write( "x + 0 + z = 4.00 = 4<BR>\n" );
document.write( "x + y + 0 = 4.25 = 17/4 multiply all times 4 to get rid of the fraction<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "2x + 2y + 2z = 11<BR>\n" );
document.write( "x + 0y + z = 4<BR>\n" );
document.write( "4x + 4y + 0z = 17<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "Swap rows 1 and 2:<BR>\n" );
document.write( "x + 0y + z = 4<BR>\n" );
document.write( "2x + 2y + 2z = 11<BR>\n" );
document.write( "4x + 4y + 0z = 17<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "Multiply the first equation times -2 and add to the 2nd equation:<BR>\n" );
document.write( "-2x + -0y + -2z = -8<BR>\n" );
document.write( "+2x + 2y + 2z = 11<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "0x + 2y + 0z = 3<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "now we have:<BR>\n" );
document.write( "x + z = 4<BR>\n" );
document.write( "2y = 3<BR>\n" );
document.write( "4x + 4y = 17<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "multiply the firs equation times -4 and add to the 3rd equation:<BR>\n" );
document.write( "-4x + 0y -4z = -16<BR>\n" );
document.write( "+ <BR>\n" );
document.write( "4x + 4y + 0z = 17<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "0x + 4y + -4z = 1<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "now we have:<BR>\n" );
document.write( "x + z = 4<BR>\n" );
document.write( "2y = 3<BR>\n" );
document.write( "4y - 4z = 1<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "swap rows 2 and 3:<BR>\n" );
document.write( "x + z = 4<BR>\n" );
document.write( "4y - 4z = 1<BR>\n" );
document.write( "2y = 3; y = 3/2<BR>\n" );
document.write( "Now that we know the value of y, let's find z:<BR>\n" );
document.write( "4y - 4z = 1<BR>\n" );
document.write( "4(3/2) - 4z = 1<BR>\n" );
document.write( "6-4z = 1 <BR>\n" );
document.write( "-4z = -5<BR>\n" );
document.write( "z = 5/4<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "Now in the first equation solve for x by substituting y= 3/2 and z = 5/4. You can do this yourself, you should get 11/4 so that:<BR>\n" );
document.write( "burger = 11/4 = $2.75<BR>\n" );
document.write( "fries = 3/2 = $1.50<BR>\n" );
document.write( "drink = 5/4 = $1.25<BR>\n" );
document.write( ":<BR>\n" );
document.write( "P.s. you can also solve this problem with a system of matrices using Cramer's Rule but you didn't say.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Happy learning!\r<BR>\n" );
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document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
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