document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171322>Question 1171322</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A stage theater sold tickets for $ 300. Senior citizens received a discount of 30%, and paid only $ 210. On the initial showing, the theater sold 250 tickets and registered a total of $ 66,000. How many of each type tickets were sold? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796270 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=796270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "First, a typical algebraic setup for solving the problem....<br><BR>\n" );
document.write( "x = number of senior tickets<BR>\n" );
document.write( "250-x = number of regular tickets<br><BR>\n" );
document.write( "Total ticket sales was $66,000:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%28x%29%2B300%28250-x%29+=+66000 ALIGN=MIDDLE  ALT=\"210%28x%29%2B300%28250-x%29+=+66000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve for x using basic algebra; then use that value to find the numbers of each kind of ticket.  I leave it to you to finish solving the problem by that method.<br><BR>\n" );
document.write( "Here is an alternative method for solving \"mixture\" problems like this that I prefer, because (for me) I get to the answer faster and with less effort.<br><BR>\n" );
document.write( "(1) Determine that the average ticket price, for $66,000 from 250 tickets, is $66000/250 = $264.<BR>\n" );
document.write( "(2) Look at the three prices $210, $264, and $300 on a number line and use simple calculations to determine that $264 is 54/90 = 6/10 = 3/5 of the way from $210 to $300.<BR>\n" );
document.write( "(3) That means 3/5 of the tickets were the higher priced tickets.<br><BR>\n" );
document.write( "ANSWER: 3/5 of 250 tickets, or 150 tickets, were regular tickets; the other 100 tickets were senior tickets.<br><BR>\n" );
document.write( "CHECK: 150(300)+100(210) = 45000+21000 = 66000<br><BR>\n" );
document.write( " </SPAN>\n" );
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