document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102892>Question 102892</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tickets for a play at the community theater cost $12 for an adult and $4 for a child.  If 130 tickets were sold and the total receipts were $840, how many of each type of 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 #74839 by </B><A HREF=/tutors/aboutme.mpl?userid=doukungfoo><B>doukungfoo(195)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=doukungfoo><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=doukungfoo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=74839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the number of adult tickets sold<BR>\n" );
document.write( "let y equal the number of child tickets sold<BR>\n" );
document.write( "we are told that there were a total of 130 tickets sold so<BR>\n" );
document.write( "x + y = 130<BR>\n" );
document.write( "we are also told that adult tickets cost $12 and child tickets cost $4<BR>\n" );
document.write( "and the total receipts were $840 so this means that <BR>\n" );
document.write( "12x + 4y = 840<BR>\n" );
document.write( "In other words $12 times the number of adult tickets sold plus $4 times the number of child tickets sold equals $840<BR>\n" );
document.write( "Ok so now we have a system of equations that we can use to solve for x and y<BR>\n" );
document.write( "I will demonstrate how to solve the system by using the substitution method.<BR>\n" );
document.write( "Lets take the first equation and set it equal to x<BR>\n" );
document.write( "x + y = 130<BR>\n" );
document.write( "To do this subtract y from both sides of the equal sign<BR>\n" );
document.write( "x + y - y = 130 - y<BR>\n" );
document.write( "The y's on the left side cancel out and we are left with<BR>\n" );
document.write( "x = 130 - y<BR>\n" );
document.write( "now take the second equation and substitute x with 130-y and solve for y<BR>\n" );
document.write( "12x + 4y = 840<BR>\n" );
document.write( "12(130-y) + 4y = 840<BR>\n" );
document.write( "multiply 12 across (130-y)<BR>\n" );
document.write( "1560 - 12y + 4y = 840<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "1560 - 8y = 840<BR>\n" );
document.write( "subtract 1560 from both sides<BR>\n" );
document.write( "1560 - 1560 - 8y = 840 - 1560<BR>\n" );
document.write( "0 - 8y = -720<BR>\n" );
document.write( "-8y = -720<BR>\n" );
document.write( "divide both sides by -8<BR>\n" );
document.write( "-8y/-8 = -720/-8<BR>\n" );
document.write( "y = 90<BR>\n" );
document.write( "<b>Answer: The theater sold 90 child tickets</b><BR>\n" );
document.write( "Now use this to find out how many adult tickets were sold<BR>\n" );
document.write( "x + y = 130<BR>\n" );
document.write( "x + 90 = 130<BR>\n" );
document.write( "x = 130 - 90<BR>\n" );
document.write( "x = 40<BR>\n" );
document.write( "<b>Answer: The theater sold 40 adult tickets</b><BR>\n" );
document.write( "Check both answers in both equations<BR>\n" );
document.write( "x + y = 130<BR>\n" );
document.write( "40 + 90 = 130<BR>\n" );
document.write( "130 = 130<BR>\n" );
document.write( "AND<BR>\n" );
document.write( "12x + 4y = 840<BR>\n" );
document.write( "12(40) + 4(90) = 840<BR>\n" );
document.write( "480 + 360 = 840<BR>\n" );
document.write( "840 = 840\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );