document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825199>Question 825199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A local movie theater charges $12 for an adult ticket and $10 for a child’s ticket. A group of <BR>\n" );
document.write( "eight people spent a total of $86 on tickets to a movie. How many adults and how many <BR>\n" );
document.write( "children were in the group? <BR>\n" );
document.write( " <BR>\n" );
document.write( "a. Write a system of linear equations based on the description. Use x to represent the <BR>\n" );
document.write( "number of adults and y to represent the number of children.  <BR>\n" );
document.write( "b. Solve the system using the elimination method. Show all the steps leading to your <BR>\n" );
document.write( "answer.  <BR>\n" );
document.write( "c. Write 1-2 sentences to explain what the solution means for this situation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497128 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "x = number of adult tickets purchased<BR>\n" );
document.write( "y = number of child tickets purchased<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x + y = 8<BR>\n" );
document.write( "12x + 10y = 86<BR>\n" );
document.write( "---<BR>\n" );
document.write( "copy and paste the above linear system in standard form into this matrix-method solver:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solution by matrix method:<BR>\n" );
document.write( "x = number of adult tickets purchased = 3<BR>\n" );
document.write( "y = number of child tickets purchased = 5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "system matrix<BR>\n" );
document.write( "1 1<BR>\n" );
document.write( "12 10<BR>\n" );
document.write( "---<BR>\n" );
document.write( "inverse of system matrix<BR>\n" );
document.write( "-5 0.5<BR>\n" );
document.write( "6 -0.5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "determinant of system matrix = -2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "now solve by elimination:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(x + y = 8)(-10)<BR>\n" );
document.write( "12x + 10y = 86<BR>\n" );
document.write( "---<BR>\n" );
document.write( "-10x - 10y = -80<BR>\n" );
document.write( "12x + 10y = 86<BR>\n" );
document.write( "---<BR>\n" );
document.write( "add the system:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2x = 6<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x + y = 8<BR>\n" );
document.write( "3 + y = 8<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solution by elimination method:<BR>\n" );
document.write( "x = number of adult tickets purchased = 3<BR>\n" );
document.write( "y = number of child tickets purchased = 5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "solution by matrix method agrees with solution by elimination method<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the solution means that 3 adult tickets and 5 child tickets were purchased.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );