document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160648>Question 1160648</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York.  Three adults and four children must pay $ 111.  Two adults and three children must pay $ 79.  Find the price of the​ adult's ticket and 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 #784050 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=784050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Although not typical, here is an alternative solution method using elimination.<br><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2B4c+=+111 ALIGN=MIDDLE  ALT=\"3a%2B4c+=+111\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B3c+=+79 ALIGN=MIDDLE  ALT=\"2a%2B3c+=+79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Subtract (2) from (1):<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc+=+32 ALIGN=MIDDLE  ALT=\"a%2Bc+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now double (3) and subtract from (2):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B3c+=+79 ALIGN=MIDDLE  ALT=\"2a%2B3c+=+79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B2c+=+64 ALIGN=MIDDLE  ALT=\"2a%2B2c+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+15 ALIGN=MIDDLE  ALT=\"c+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Plug c=15 into (3) to find a=17.<br><BR>\n" );
document.write( "ANSWER: adult ticket costs $17; child ticket costs $15.<br><BR>\n" );
document.write( "This method can be used -- either formally, as above, of informally, as below, because the difference between the two given cases is 1 adult and 1 child.<br><BR>\n" );
document.write( "This variation of a formal algebraic solution using elimination exactly follows an informal solution obtained by logical reasoning:<br><BR>\n" );
document.write( "3 adults and 4 children cost $111<BR>\n" );
document.write( "2 adults and 3 children cost $79<br><BR>\n" );
document.write( "Therefore, continuing the \"pattern\" of 1 less adult and 1 less children for $32 less...<br><BR>\n" );
document.write( "1 adult and 2 children cost $47<BR>\n" );
document.write( "0 adult and 1 child cost $15<br><BR>\n" );
document.write( "ANSWER: child $15; adult $32-$15 = $17<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );