document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74620>Question 74620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Adult tickets for a play cost $9 and child tickets cost $8.  If there were 23 people at a performance and the theater collected $193 from ticket sales, how many children attended the play? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53597 by </B><A HREF=/tutors/aboutme.mpl?userid=rvaught><B>rvaught(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rvaught><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=53597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What you want to do here is to solve a system of equations by setting up two linear equations, with your x and y variables aligned on the same side.  Let x represent adult tickets, and y represent child tickets.  Then, <BR>\n" );
document.write( "x + y = 23  (means that the number of 'x' tickets plus the number of 'y' tickets total 23).  <BR>\n" );
document.write( "Also, 9x+8y=193 (means that the number of x tickets, times the cost of $9 each, plus the number of y tickets, times the cost of $8 each, totalled $193).  \r<BR>\n" );
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document.write( "Now, line the two equations up with one above the other, and use one of the methods for solving systems of equations:<BR>\n" );
document.write( "  x+y=23<BR>\n" );
document.write( "9x+8y=193\r<BR>\n" );
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document.write( "Substitution would probably be your best bet here, since the first equation has variables with coefficients of 1.  So, solve for one of the variables.  If x+y=23, then subtract y from both sides to get x=23-y.  Plug this value into the second equation:  9(23-y)+8y=193.  Now, you only have one variable, which can be solved for.  Find the value of y.  First, distribute the 9.  Then, <BR>\n" );
document.write( "     9(23-y)+8y=193<BR>\n" );
document.write( "(9*23)-(9*y)+8y=193<BR>\n" );
document.write( "      207-9y+8y=193 <BR>\n" );
document.write( "          207-y=193<BR>\n" );
document.write( "              y=14 <BR>\n" );
document.write( "This tells us that 14 'child' tickets were sold.  We can plug this value into the first equation to find that if 14 'child' tickets were sold, and a total of 23 tickets were sold, then 9 'adult' tickets were sold (23-14=9).  \r<BR>\n" );
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document.write( "Going back to the question, it asks for the number of children that attended.  We found that 14 'child' tickets were sold.  \r<BR>\n" );
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document.write( "Hope this helps! </SPAN>\n" );
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