document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204986>Question 1204986</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Patricia's school is selling tickets to the school play. On the first day of ticket sales the school sold 6 children tickets and 5 adults tickets for a total of $130.00 The school collected $284.00 on the second day by selling 12 children tickets  and 13 adult tickets. What was the price of each type of ticket? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841562 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=841562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Fact 1: <font color=blue>sold 6 children tickets and 5 adults tickets for a total of $130.00</font><BR>\n" );
document.write( "Fact 2: <font color=blue>school collected $284.00 on the second day by selling 12 children tickets and 13 adult tickets</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Fact 1 translates to the equation 6x+5y = 130<BR>\n" );
document.write( "Fact 2 translates to the equation 12x+13y = 284<BR>\n" );
document.write( "x = price of child ticket<BR>\n" );
document.write( "y = price of an adult ticket\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's double everything in the 1st equation to get 12x+10y = 260\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have this equivalent system<BR>\n" );
document.write( "12x+10y = 260<BR>\n" );
document.write( "12x+13y = 284\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract straight down to get -3y = -24 which solves to y = 8<BR>\n" );
document.write( "It costs $8 per adult.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then use this to find x.<BR>\n" );
document.write( "6x+5y = 130<BR>\n" );
document.write( "6x+5*8 = 130<BR>\n" );
document.write( "6x+40 = 130<BR>\n" );
document.write( "6x = 130-40<BR>\n" );
document.write( "6x = 90<BR>\n" );
document.write( "x = 90/6<BR>\n" );
document.write( "x = 15<BR>\n" );
document.write( "It costs $15 per child.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=red>Ticket prices:<BR>\n" );
document.write( "child = $15<BR>\n" );
document.write( "adult = $8</font><BR>\n" );
document.write( "It's interesting that the child ticket costs more compared to the adult, when normally math problems like this have it flipped around (to reflect the real world that does the same thing). Of course these are just hypothetical numbers anyway.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's check fact 1<BR>\n" );
document.write( "6x+5y = 130<BR>\n" );
document.write( "6*15+5*8 = 130<BR>\n" );
document.write( "90+40 = 130<BR>\n" );
document.write( "130 = 130 ... works out<BR>\n" );
document.write( "And now fact 2<BR>\n" );
document.write( "12x+13y = 284<BR>\n" );
document.write( "12*15+13*8 = 284<BR>\n" );
document.write( "180+104 = 284<BR>\n" );
document.write( "284 = 284 .... verified as well<BR>\n" );
document.write( "The answers are fully confirmed.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );