document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=857651>Question 857651</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a movie theater a family buys 2 adult tickets and 1 child ticket for a total of $18.00. Another family buys 1 adult ticket and 3 child tickets for a total of $21.50. What is a linear equation that can be used to determine the price of an adult ticket and the price of a child ticket? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516705 by </B><A HREF=/tutors/aboutme.mpl?userid=JulietG><B>JulietG(1812)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JulietG><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=JulietG><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=516705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2A + 1C = 18<BR>\n" );
document.write( "1A + 3C = 21.50<BR>\n" );
document.write( "Add them together<BR>\n" );
document.write( "3A + 4C = 39.50<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Here's my brain's way of going about it.<BR>\n" );
document.write( "We know that an adult's ticket ends in .50 (the first equation is even; the second is odd).<BR>\n" );
document.write( "We can assume that an adult ticket is priced higher than a child's.  With that assumption...<BR>\n" );
document.write( "We can tell that an adult ticket is no more than 7.50 and no less than 6.50.<BR>\n" );
document.write( "Plug the values in to see:<BR>\n" );
document.write( "2(6.50) + C = 18.  C would be 5<BR>\n" );
document.write( "2(7.50) + C = 18.  C would be 3<BR>\n" );
document.write( "Let's try the 7.50 into the second equation:<BR>\n" );
document.write( "7.50 + 9 does not equal 21.50.  Oops!<BR>\n" );
document.write( "What about the other?<BR>\n" );
document.write( "6.50 + 15 does equal 21.50.  Success!<BR>\n" );
document.write( "The adult ticket is $6.50 and the child's ticket is $5 (must be a matinee!) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );