document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148837>Question 1148837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following problem using two variables and a system of two equations. Solve the system by the method of your choice.<BR>\n" );
document.write( "The City Zoo has different admission prices for adults and children. When three adults and two children went to the​ zoo, the bill was​ $78.05. If two adults and three children got in for ​$73.90​, then what is the price of an​ adult's ticket and what is the price of a​ child's​ ticket? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770169 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=770169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = the price of an adult ticket.<BR>\n" );
document.write( "y = the price of a child ticket.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have two equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "3x + 2y = 78.05<BR>\n" );
document.write( "2x + 3y = 73.90\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of the first equation by 2 and multiply both sides of the second equation to 3 to get:<BR>\n" );
document.write( "6X + 4Y = 156.10<BR>\n" );
document.write( "6X + 9Y = 221.70<BR>\n" );
document.write( "subtract the first equation from the second to get:<BR>\n" );
document.write( "5y = 65.60<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 13.12<BR>\n" );
document.write( "replace y in the first original equation of 3x + 2y = 78.05 and solve for x to get:<BR>\n" );
document.write( "x = 17.27\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have:<BR>\n" );
document.write( "x = 17.27<BR>\n" );
document.write( "y = 13.12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "go back to the original two equations to get:<BR>\n" );
document.write( "3x + 2y = 78.05 becomes 51.81 + 26.24 = 78.05 which becomes 78.05 = 78.05, which is true.<BR>\n" );
document.write( "2x + 3y = 73.90 becomes 34.54 + 39.36 = 73.90 which becomes 73.90 = 73.90, which is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both original equations are true when x = 17.27 and y = 13.13.<BR>\n" );
document.write( "this confirms those values are good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is that the price of an adult ticket is 17.27 and the price of a child ticket is 13.12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );