document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138773>Question 1138773</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A local concert sells out for their show. They sell all 500 tickets for a total purse of $8,070.00. The tickets were priced at $15 for students (s), $12 for children (c), and $18 for adults (a). If the band sold three times as many adult tickets as children’s tickets, how many of each type was sold?\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 #756560 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "This problem can be a good example for comparing the method of solving the problem with three variables (as suggested by the statement of the problem) to the method of solving it with a single variable.<br><BR>\n" );
document.write( "While it is important to know how to solve a problem involving a system of equations in several variables, very often the amount of effort required to solve the problem is far less with a single equation in one variable.<br><BR>\n" );
document.write( "A solution using 3 variables....<br><BR>\n" );
document.write( "c = number of children's tickets<BR>\n" );
document.write( "s = number of student tickets<BR>\n" );
document.write( "a = number of adult tickets<br><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bs%2Bc+=+500 ALIGN=MIDDLE  ALT=\"a%2Bs%2Bc+=+500\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the total number of tickets was 500<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+3c ALIGN=MIDDLE  ALT=\"a+=+3c\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the number of adult tickets was 3 times the number of children's tickets<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12c%2B15s%2B18a+=+8070 ALIGN=MIDDLE  ALT=\"12c%2B15s%2B18a+=+8070\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the total cost of the tickets was $8070<br><BR>\n" );
document.write( "Substitute (2) in (1) and (3) to eliminate a, giving two equations in s and c:<br><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3c%2Bs%2Bc+=+500 ALIGN=MIDDLE  ALT=\"3c%2Bs%2Bc+=+500\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2B4c+=+500 ALIGN=MIDDLE  ALT=\"s%2B4c+=+500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12c%2B15s%2B18%283c%29+=+8070 ALIGN=MIDDLE  ALT=\"12c%2B15s%2B18%283c%29+=+8070\"   DISABLED_style= \"max-width:90%; height:auto;\" > -->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15s%2B66c+=+8070 ALIGN=MIDDLE  ALT=\"15s%2B66c+=+8070\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Eliminate s between (4) and (5) by multiplying (4) by -15 and adding:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15s-60c+=+-7500 ALIGN=MIDDLE  ALT=\"-15s-60c+=+-7500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15s%2B66c+=+8070 ALIGN=MIDDLE  ALT=\"15s%2B66c+=+8070\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c+=+570 ALIGN=MIDDLE  ALT=\"6c+=+570\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+95 ALIGN=MIDDLE  ALT=\"c+=+95\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The number of children's tickets was c = 95.<br><BR>\n" );
document.write( "Then the number of adult tickets was 3c = 285.<br><BR>\n" );
document.write( "The total number of adult and children's tickets was 95+285 = 380; so the number of student tickets was 500-380 = 120.<br><BR>\n" );
document.write( "ANSWER: 95 children's tickets, 120 student tickets, 285 adult tickets.<br><BR>\n" );
document.write( "A solution using one variable....<br><BR>\n" );
document.write( "let x = number of children's tickets<BR>\n" );
document.write( "then 3x = number of adult tickets  (3 times as many as children's)<BR>\n" );
document.write( "and (500-4x) = number of student tickets  (the total of 500, minus the adult and children's tickets)<br><BR>\n" );
document.write( "The total cost was $8070:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B15%28500-4x%29%2B18%283x%29+=+8070 ALIGN=MIDDLE  ALT=\"12x%2B15%28500-4x%29%2B18%283x%29+=+8070\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B7500-60x%2B54x+=+8070 ALIGN=MIDDLE  ALT=\"12x%2B7500-60x%2B54x+=+8070\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+=+570 ALIGN=MIDDLE  ALT=\"6x+=+570\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+95 ALIGN=MIDDLE  ALT=\"x+=+95\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "children: x = 95<BR>\n" );
document.write( "students: 500-4x = 500-380 = 120<BR>\n" );
document.write( "adults: 3x = 285 </SPAN>\n" );
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