document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201132>Question 1201132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Formulate a system of equations for the situation below and solve.\r<BR>\n" );
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document.write( "A theater has a seating capacity of 750 and charges $4 for children, $6 for students, and $8 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $4600. How many children attended the show?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835631 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Probably a formal algebraic solution is what you were supposed to find.  You have received several responses that show different ways to do that, using either three variables or just one.<br><BR>\n" );
document.write( "While you should be able to solve the problem using formal algebra, you will get probably better mental exercise and better experience in problem solving by solving the whole problem informally, using logical reasoning and mental arithmetic.<br><BR>\n" );
document.write( "As one of the tutors points out, careful reading of the problem followed by logical reasoning shows that 1/3 of the tickets were adult tickets and 2/3 were the combined children and student tickets.  1/3 of the total 750 is 250; and 250 adult tickets at $8 each makes $2000 in sales.  So the other 500 tickets, at $4 or $6 each, combine for a total of $2600 in sales.<br><BR>\n" );
document.write( "To find the number of child and student tickets sold, you can do the following, again using only logical reasoning and some mental arithmetic.<br><BR>\n" );
document.write( "If all 500 remaining tickets had been child tickets, the total sales for those tickets would have been $2000; if all 500 had been student tickets, that total would have been $3000.  The actual total sales from those 500 tickets was $2600.<br><BR>\n" );
document.write( "Use mental arithmetic to see that the actual total of $2600 is 600/1000 = 3/5 of the way from $2000 to $3000; that means 3/5 of those 500 tickets were the higher-priced student tickets.  So 2/5 of those 500 tickets were the children's tickets.<br><BR>\n" );
document.write( "ANSWER: # of children = 2/5 of 500 = 200<br><BR>\n" );
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