document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109402>Question 109402</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tickets for an event cost $5 for children, $11 for adults, and $6 for senior citizens.  The total ticket sales were $1750.  There were 50 more adult tickets sold than child tickets, and the number of senior citizens tickets were 4 times the number of child tickets.  How many of each ticket were sold? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79833 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=79833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=number of children tickets sold<BR>\n" );
document.write( "And y=number of adult tickets sold<BR>\n" );
document.write( "And z=number of senior tickets sold\r<BR>\n" );
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document.write( "Now the problem tells us the following:\r<BR>\n" );
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document.write( "5x+11y+6z=1750-------------------------------eq1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "y=x+50------------------------------------------eq2<BR>\n" );
document.write( "and<BR>\n" );
document.write( "z=4x----------------------------------------------eq3\r<BR>\n" );
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document.write( "Three equations, three unknowns.  Lets solve by substitution.  We will substitute the value for y in eq2 and the value for z in eq3 into eq1 and we get:\r<BR>\n" );
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document.write( "5x+11(x+50)+6(4x)=1750 get rid of parens<BR>\n" );
document.write( "5x+11x+550+24x=1750  subtract 550 from both sides\r<BR>\n" );
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document.write( "5x+11x+550-550+24x=1750-550  collect like terms\r<BR>\n" );
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document.write( "40x=1200   divide both sides by 40 <BR>\n" );
document.write( "x=30------------------------------------number of children tickets sold<BR>\n" );
document.write( "substitute x=30 into eq2:<BR>\n" );
document.write( "y=30+50=80-----------------------------number of adult tickets sold\r<BR>\n" );
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document.write( "substitute x=30 into eq3 and we have:\r<BR>\n" );
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document.write( "z=4*30=120------------------------------number of senior tickets sold\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "From eq1:\r<BR>\n" );
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document.write( "5*30+11*80+6*120=1750<BR>\n" );
document.write( "150+880+720=1750<BR>\n" );
document.write( "1750=1750\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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