document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=55428>Question 55428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with these two word problems.  I can not figure them out.\r<BR>\n" );
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document.write( "1. Adult tickets for a play cost $4 and child tickets cost $1.  If there were 23 people at a performance and the theater collected $80 from ticket sales, how many children attended the play?\r<BR>\n" );
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document.write( "2.Tickets for an event cost $4 for children, $12 for adults, and $7 for senior citizens.  The total ticket sales were $1920.  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 #37614 by </B><A HREF=/tutors/aboutme.mpl?userid=piyu><B>piyu(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=piyu><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=37614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Adult tickets for a play cost $4 and child tickets cost $1. If there were 23 people at a performance and the theater collected $80 from ticket sales, how many children attended the play?<BR>\n" );
document.write( "ANS:<BR>\n" );
document.write( "let the no. of adults be x and the no. of children be y<BR>\n" );
document.write( "the total no. of people who attended the play = 23<BR>\n" );
document.write( "which means x+y=23<BR>\n" );
document.write( "the cost of an adult ticketis $4 and hence the total collections from adult tickets=4x<BR>\n" );
document.write( "similarly the total collections from child tickets is $1 per child= y<BR>\n" );
document.write( "the total colltecions is $80. which implies <BR>\n" );
document.write( "4x+y=80. solving the system of linear equations<BR>\n" );
document.write( "4x+y=80<BR>\n" );
document.write( "x+y=23<BR>\n" );
document.write( "we get y=4 (i.e) the no. of children who attended the play is 4\r<BR>\n" );
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document.write( "2.Tickets for an event cost $4 for children, $12 for adults, and $7 for senior citizens.  The total ticket sales were $1920.  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?<BR>\n" );
document.write( "ANS:<BR>\n" );
document.write( "assume the no. of childern to be x, no. of adults to be y and the no. of senior citizens to be z.<BR>\n" );
document.write( "the cost per ticket is $4 for children, $12 for adults, and $7 for senior citizens. the total ticket sales amounted to $1920. which is nothing but<BR>\n" );
document.write( "4x+12y+7z=1920           (equation 1)\r<BR>\n" );
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document.write( "given that 50 more adult tickets were sold than child tickets<BR>\n" );
document.write( "y-x=50 or y=50-x         (equation 2)\r<BR>\n" );
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document.write( "the number of senior citizens tickets were 4 times the number of child tickets.<BR>\n" );
document.write( "z=4x                     (equation 3)\r<BR>\n" );
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document.write( "4x+12y+7z=1920(from equation 1)<BR>\n" );
document.write( "substituting for y and z from equations 2&3, we have<BR>\n" );
document.write( "4x+12(x+50)+7(4x)=1920<BR>\n" );
document.write( "4x+12x+600+28x   =1920<BR>\n" );
document.write( "44x+600          =1920<BR>\n" );
document.write( "44x=1920-600<BR>\n" );
document.write( "44x=1320<BR>\n" );
document.write( "x=1320/44<BR>\n" );
document.write( "x=30\r<BR>\n" );
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document.write( "from equation 2 <BR>\n" );
document.write( "y=50+x  (i.e)y=50+30<BR>\n" );
document.write( "y=80\r<BR>\n" );
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document.write( "from equation 3<BR>\n" );
document.write( "z=4x or z=4(30)<BR>\n" );
document.write( "z=120\r<BR>\n" );
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document.write( "hence the no. of child tickets sold is 30, no. of adult tickets sold is 80 and the no. of senior citizen tickets sold is 120\r<BR>\n" );
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document.write( " </SPAN>\n" );
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