document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178546>Question 1178546</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 $136. <BR>\n" );
document.write( "Two adults and three children must pay $97. 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 #807884 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=807884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are of course many paths to a solution of this problem using formal algebra.<br><BR>\n" );
document.write( "Here is an unusual path that makes solving this particular problem easy, because of exactly how the given information is presented.  We have<br><BR>\n" );
document.write( "(1) 3a+4d=136<BR>\n" );
document.write( "(2) 2a+3d=97<br><BR>\n" );
document.write( "A typical solution using elimination would have you multiply the first equation by 2 and the second by -3, then adding the two resulting equations to eliminate a.<br><BR>\n" );
document.write( "But there is a faster and easier path to the solution of this particular pair of equations.<br><BR>\n" );
document.write( "Compare the two given equations:<BR>\n" );
document.write( "(3) a+d=39<br><BR>\n" );
document.write( "double that:<BR>\n" );
document.write( "(4) 2a+2d=78<br><BR>\n" );
document.write( "Compare (4) and (2):<BR>\n" );
document.write( "d=19<br><BR>\n" );
document.write( "Plug that into (3) to find a=20.<br><BR>\n" );
document.write( "ANSWER: Adult fare $20; child fare $19.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "3(20)+4(19)=60+76=136<BR>\n" );
document.write( "2(20)+3(19)=40+57=97<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );