document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328752>Question 328752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please walk me through this?\r<BR>\n" );
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document.write( "The receipts for one showing of a movie were $540 for an audience of 120 people. The ticket prices are given in the table. If twice as many children's tickets as general admission tickets were purchased, how many of each type of ticket were sold?\r<BR>\n" );
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document.write( "Ticket Prices<BR>\n" );
document.write( "Children  $4<BR>\n" );
document.write( "General Admission  $6<BR>\n" );
document.write( "Seniors	  $4\r<BR>\n" );
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document.write( "___ children's tickets<BR>\n" );
document.write( "___ general admission tickets<BR>\n" );
document.write( "___ senior tickets \r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235541 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=235541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The receipts for one showing of a movie were $540 for an audience of 120 people. The ticket prices are given in the table. If twice as many children tickets as general admission tickets were purchased, how many of each type of ticket were sold?\r<BR>\n" );
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document.write( "Ticket Prices<BR>\n" );
document.write( "Children  $4<BR>\n" );
document.write( "General Admission  $6<BR>\n" );
document.write( "Seniors	  $4\r<BR>\n" );
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document.write( "Let c = number of children tickets<BR>\n" );
document.write( "Let g = number of general admission tickets<BR>\n" );
document.write( "Let s = number of senior tickets.\r<BR>\n" );
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document.write( "Total revenue = 4*c + 6*g + 4*s = 540\r<BR>\n" );
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document.write( "Total number of people attending = c + g + s = 120\r<BR>\n" );
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document.write( "Solve these 2 equations simultaneously and you should be able to find the number of c and g and s.\r<BR>\n" );
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document.write( "Only problem is you have 2 equations in 3 unknowns.\r<BR>\n" );
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document.write( "You need either 3 equations in 3 unknowns or 2 equations in 2 unknowns to get an exact solution.\r<BR>\n" );
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document.write( "Fortunately, they tell you a relationship that you can use to reduce the number of unknowns.\r<BR>\n" );
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document.write( "That relationship is that 2 times the number of children tickets sold was twice the number of general admission tickets sold.\r<BR>\n" );
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document.write( "In algebraic form, this means the c = 2*g\r<BR>\n" );
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document.write( "You can substitute for c in your equations to reduce the number of unknowns from 3 to 2.\r<BR>\n" );
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document.write( "Your equations were:\r<BR>\n" );
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document.write( "Total revenue = 4*c + 6*g + 4*s = 540<BR>\n" );
document.write( "Total number of people attending = c + g + s = 120\r<BR>\n" );
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document.write( "Substitute 2*g for c in both of these equations to get:\r<BR>\n" );
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document.write( "4*2*g + 6*g + 4*s = 520<BR>\n" );
document.write( "2*g + g + s = 120\r<BR>\n" );
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document.write( "Simplify and combine like terms to get:\r<BR>\n" );
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document.write( "14*g + 4*s = 520<BR>\n" );
document.write( "3*g + s = 120\r<BR>\n" );
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document.write( "Now you have 2 equations in 2 unknowns that can be solved for a unique solution.\r<BR>\n" );
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document.write( "If you multiply the second equation by 4, then you will be able to subtract one equation from the other to get down to 1 unknown in 1 equation.\r<BR>\n" );
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document.write( "After multiplying the second equation by 4, you get:\r<BR>\n" );
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document.write( "14*g + 4*s = 520<BR>\n" );
document.write( "12*g + 4*s = 480\r<BR>\n" );
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document.write( "Subtract the second equation from the first equation to get:\r<BR>\n" );
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document.write( "2*g = 40\r<BR>\n" );
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document.write( "Divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "g = 20\r<BR>\n" );
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document.write( "Since c = 2*g, this means that c = 40\r<BR>\n" );
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document.write( "You can substitute in either original equation to find s.\r<BR>\n" );
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document.write( "You had c + g + s = 120\r<BR>\n" );
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document.write( "Substitute to get 60 + s = 120\r<BR>\n" );
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document.write( "Solve for s to get s = 60\r<BR>\n" );
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document.write( "you now have c = 40, g = 20, s = 60\r<BR>\n" );
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document.write( "Confirm this solution is correct by substituting in the other original equation.\r<BR>\n" );
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document.write( "That equation is:\r<BR>\n" );
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document.write( "4*c + 6*g + 4*s = 540\r<BR>\n" );
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document.write( "Substituting, you get:\r<BR>\n" );
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document.write( "160 + 120 + 240 = 520 which is correct, confirming that your solution is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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