document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166731>Question 1166731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. An adult ticket costs as much as the combined cost of a student ticket and a child ticket. You purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23. What is the price per ticket for a student ticket?\r<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 #791247 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=791247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let A = the cost of an adult ticket.<BR>\n" );
document.write( "let S = the cost of a student ticket.<BR>\n" );
document.write( "let C = the cost of a child ticket.\r<BR>\n" );
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document.write( "your two formulas are:<BR>\n" );
document.write( "2A + S + C = 15<BR>\n" );
document.write( "A + 4S + 2C = 23\r<BR>\n" );
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document.write( "you are given A = S + C because one adult ticket is the same as the combined cost of a student and child ticket.\r<BR>\n" );
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document.write( "replace A in the two equations with S + C to get:<BR>\n" );
document.write( "2 * (S + C) + S + C = 15<BR>\n" );
document.write( "S + C + 4S + 2C = 23\r<BR>\n" );
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document.write( "simplify and combine like terms to get:<BR>\n" );
document.write( "3S + 3C = 15<BR>\n" );
document.write( "5S + 3C = 23\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:<BR>\n" );
document.write( "2S = 8\r<BR>\n" );
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document.write( "solve for S to get:<BR>\n" );
document.write( "S = 4\r<BR>\n" );
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document.write( "in the first first equation of 3S + 3C = 15, replace S with 4 to get:<BR>\n" );
document.write( "3 * 4 + 3C = 15<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "12 + 3C = 15<BR>\n" );
document.write( "subtract 12 from both sides of this equation and simpliy to get:<BR>\n" );
document.write( "3C = 3<BR>\n" );
document.write( "solve for C to get:<BR>\n" );
document.write( "C = 1\r<BR>\n" );
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document.write( "you have:<BR>\n" );
document.write( "S = 4<BR>\n" );
document.write( "C = 1\r<BR>\n" );
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document.write( "since A = S + C, you also have:<BR>\n" );
document.write( "A = 5\r<BR>\n" );
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document.write( "in your two original equations, replace A with 5 and S with 4 and C with 1 to get:<BR>\n" );
document.write( "2A + S + C = 15 becomes 2*5 + 4 + 1 = 15 which becomes 15 = 15 which is true.<BR>\n" );
document.write( "A + 4S + 2C = 23 becomes 5 + 4*4 + 2*1 = 23 which becomes 5 + 16 + 2 = 23 which becomes 23 = 23 which is also true.<BR>\n" );
document.write( "this confirms the values for A and S and C are good.\r<BR>\n" );
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document.write( "your solution is that S = 4 which means that the price of a student ticket is 4 dollars.\r<BR>\n" );
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