document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828935>Question 828935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The attendance at a rock concert was 6700 people. The tickets for the concer cost $40 for floor seats and $25 for all other seats. The total income of ticket sales was $185,500. write a linear system that models this situation. Solve the system using Cramer's rule, using the substitution method, and using the elimination method. Compare the methods, and explain which one you perfer in this situation. I did the elimination and substitute methods, but I cannot figure out how to set up the Cramer part. Any help would be appreciated </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499597 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=499597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x +y = 6700<BR>\n" );
document.write( "40x +25y = 185500<BR>\n" );
document.write( "we have a 2 by 2 matrix and single column solution vector<BR>\n" );
document.write( "we calculate the determinant (D) of a two by two matrix according to this formula<BR>\n" );
document.write( "| a  b |<BR>\n" );
document.write( "| c  d |<BR>\n" );
document.write( "D = ad - bc<BR>\n" );
document.write( "for our linear system of equations, the matrix is<BR>\n" );
document.write( "|  1  1 |<BR>\n" );
document.write( "| 40 25 |<BR>\n" );
document.write( "and D = (1*25) - (40*1) = -15<BR>\n" );
document.write( "now we need to replace the x column with our column solution vector<BR>\n" );
document.write( "|   6700  1 |<BR>\n" );
document.write( "| 185500 25 |<BR>\n" );
document.write( "Dx = (6700 * 25) - (185500 * 1) = -18000<BR>\n" );
document.write( "now we need to replace the y column with our column solution vector<BR>\n" );
document.write( "|  1   6700 |<BR>\n" );
document.write( "| 40 185500 |<BR>\n" );
document.write( "Dy = (1 * 185500) - (6700 * 40) = 185500 - 268000 = -82500<BR>\n" );
document.write( "now x = Dx / D = -18000 / -15 = 1200<BR>\n" );
document.write( "y = Dy / D = -82500 / -15 = 5500<BR>\n" );
document.write( "we have 1200 tickets at $40 and 5500 at $25<BR>\n" );
document.write( "check answer <BR>\n" );
document.write( "1200 +5500 = 6700<BR>\n" );
document.write( "6700 = 6700<BR>\n" );
document.write( "also<BR>\n" );
document.write( "(40*1200) + (25*5500) = 185500<BR>\n" );
document.write( "48000 + 137500 = 185500<BR>\n" );
document.write( "185500 = 185500<BR>\n" );
document.write( "answer checks   :-)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );