document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81742>Question 81742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Adult tickets for a play cost $10 and child tickets cost $3.  If there were 25 people at a performance and the theater collected $110 from ticket sales, how many adults and how many children attended the play?\r<BR>\n" );
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document.write( "Answer:  <BR>\n" );
document.write( "	___________ adults attended the play <BR>\n" );
document.write( "	___________ children attended the play\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 #58567 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=58567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two unknowns in this problem ... the number of adults and the number of children<BR>\n" );
document.write( "that attend a play.  This is a clue that you will need two equations to solve this problem.<BR>\n" );
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document.write( "As a start, let A represent the number of adults and C represent the number of children.<BR>\n" );
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document.write( "The problem tells you that 25 people attend the performance.  This tells you that if you<BR>\n" );
document.write( "add the number of adults and the number of children that attend, you should get an answer of 25.<BR>\n" );
document.write( "In equation form this becomes:<BR>\n" );
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document.write( "A + C = 25<BR>\n" );
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document.write( "This is the first of the two equations.<BR>\n" );
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document.write( "Next you can determine the amount of money taken in from adult tickets and also from children's<BR>\n" );
document.write( "tickets.  Since adult tickets are $10 each, the amount of money taken in from the sale of<BR>\n" );
document.write( "adult tickets is $10 times the number of adults that attend or 10*A.  Similarly, since <BR>\n" );
document.write( "children's tickets are $3 each, the amount of money from the sale of children's tickets is<BR>\n" );
document.write( "$3 times the number of children that attend or 3*C. The problem tells you that the total<BR>\n" );
document.write( "amount from the sale of tickets is $110. In equation form this becomes:<BR>\n" );
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document.write( "10*A + 3*C = 110<BR>\n" );
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document.write( "This is the second equation that we need.  <BR>\n" );
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document.write( "The equations can be solved by substitution.  Since the problem asks for the number of<BR>\n" );
document.write( "children that attend the play, it would help if the second equation were converted so<BR>\n" );
document.write( "that it contained only the variable C. You can do that by solving the first equation<BR>\n" );
document.write( "for A in terms of C. Start with the first equation:<BR>\n" );
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document.write( "A + C = 25<BR>\n" );
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document.write( "Subtract C from both sides to get:<BR>\n" );
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document.write( "A = 25 - C<BR>\n" );
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document.write( "Then in the second equation you can substitute 25 - C for A.  If you do that the second<BR>\n" );
document.write( "equation becomes:<BR>\n" );
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document.write( "10*(25 - C) + 3*C = 110<BR>\n" );
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document.write( "Do the distributed multiplication on the left side to get:<BR>\n" );
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document.write( "250 - 10*C + 3*C = 110<BR>\n" );
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document.write( "On the left side combine the two terms that contain C and the equation becomes:<BR>\n" );
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document.write( "250 - 7*C = 110<BR>\n" );
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document.write( "Now subtract 250 from both sides so that only the term involving C remains on the left<BR>\n" );
document.write( "side.  The subtraction of 250 from both sides results in:<BR>\n" );
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document.write( "- 7*C = 110 - 250 = - 140<BR>\n" );
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document.write( "Finally, divide both sides by -7, the multiplier of C. When you do that you get:<BR>\n" );
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document.write( "C = 20<BR>\n" );
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document.write( "So 20 children attend. (This means that of the 25 that attend 20 are children and the<BR>\n" );
document.write( "remaining 5 are adults.)<BR>\n" );
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document.write( "As a check, at $3 each for the 20 children's tickets, 3*20 equals $60 is taken in from<BR>\n" );
document.write( "the sales of childrens tickets. And at $10 each for the 5 adults that attend, the income<BR>\n" );
document.write( "from the sale of adult tickets is 10*5 = $50.  Therefore, the total income from the sale<BR>\n" );
document.write( "of tickets is $60 + $50 = $110.  That is exactly what it is supposed to be, so our answer<BR>\n" );
document.write( "checks out. 20 children attend the play and 5 adults attend.<BR>\n" );
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document.write( "Hope this helps you to understand the problem ... and how to get and solve the pair of<BR>\n" );
document.write( "equations that is needed. </SPAN>\n" );
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