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 #841561 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = price of a child ticket.<BR>\n" );
document.write( "y = price of an adult ticket.\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "6x + 5y = 130<BR>\n" );
document.write( "12x + 13y = 284\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 2 and leave the second equation as is to get:<BR>\n" );
document.write( "12x + 10y = 260<BR>\n" );
document.write( "12x + 13y = 284\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:<BR>\n" );
document.write( "3y = 24<BR>\n" );
document.write( "solve for y to get y = 8\r<BR>\n" );
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document.write( "replace y with 8 in the second equation to get:<BR>\n" );
document.write( "12x + 13*8 = 284<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "12x + 104 = 284<BR>\n" );
document.write( "subtract 104 from both sides of the equation to get:<BR>\n" );
document.write( "12x = 180<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 180/12 = 15\r<BR>\n" );
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document.write( "you have x = 15 and y = 8\r<BR>\n" );
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document.write( "go back to your original equations to see if they are true when you replace x with 15 and y with 8.\r<BR>\n" );
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document.write( "the two original equations are:<BR>\n" );
document.write( "6x + 5y = 130 becomes 6*15 + 5*8 = 130 which becomes 90 + 40 = 130 which is true.<BR>\n" );
document.write( "12x + 13y = 284 becomes 12*15 + 13*8 = 284 which becomes 180 + 104 = 284 which is also true.\r<BR>\n" );
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document.write( "the problem is satisfied when x = 15 and y = 8.<BR>\n" );
document.write( "that means the price of a child ticket is 15 and the price of an adult ticket is 8.\r<BR>\n" );
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document.write( "that's your solution.<BR>\n" );
document.write( "this appears to be counter-intuitive as you would expect the child ticket to be less than the adult ticket, but that's the way it worked out.\r<BR>\n" );
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document.write( "here's what it looks like on a graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/111701.jpg\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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