document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196453>Question 1196453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each day Sal prepares a large basket of self-serve tortilla chips in his restaurant. On Monday, 28 adult patrons and 37 child patrons ate 12.67 kg of chips. On Tuesday, 14 adult patrons and 30 child patrons ate 11.3 kg of chips. Write two equations that would be used to solve the system so that Sal would know whether adults or children eat more chips on average. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829286 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=829286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = the number of kilograms eaten by each adult on the average.<BR>\n" );
document.write( "let b = the number of kilograms eaten by each child on the average.<BR>\n" );
document.write( "you get two equations.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "28a + 37c = 12.67 kilograms<BR>\n" );
document.write( "14a + 30c = 11.3 kilograms.<BR>\n" );
document.write( "solve these two equations simultaneously to get:<BR>\n" );
document.write( "c = .43173901304<BR>\n" );
document.write( "a = -.1180124224<BR>\n" );
document.write( "confirm these values are correct by replacing a and c in both original equations to get:<BR>\n" );
document.write( "28 * -.1180124224 + 37 * .43173901304 = 12.67<BR>\n" );
document.write( "14 * -.1180124224 + 30 * .43173901304 = 11.3<BR>\n" );
document.write( "this confirms the values are correct.<BR>\n" );
document.write( "unfortunately, the value of a is less than 0 which means that you don't have a solution to this system of equations where the average number of kilograms consumed by adults and children is positive for both.<BR>\n" );
document.write( "since that is a requirement, then the system of equations does not have a common solution.<BR>\n" );
document.write( "i also solved graphically where the intersection of the lines graphed by the two equations is at the intersection of those lines.<BR>\n" );
document.write( "it confirms the common solution requires a negative value for the average number of kilograms consumed by the adults.<BR>\n" );
document.write( "since this can't be, the solution is invalid.<BR>\n" );
document.write( "here's the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/091704.jpg\"><BR>\n" );
document.write( "however, you were not asked to solve the system of equations.<BR>\n" );
document.write( "you were only asked to write two equations that could be used to solve the system.<BR>\n" );
document.write( "your solution is the two equations shown above.<BR>\n" );
document.write( "they are reproduced below for your convenience.<BR>\n" );
document.write( "28a + 37c = 12.67 kilograms<BR>\n" );
document.write( "14a + 30c = 11.3 kilograms.<BR>\n" );
document.write( "a is the average number of kilograms of chips consumed by each adult.<BR>\n" );
document.write( "c is the average number of kilograms of chips consumed by each child.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );