document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=915932>Question 915932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> helppp \r<BR>\n" );
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document.write( " Jen butler has been pricing Speed-Pass train fares for a group trip to New York.<BR>\n" );
document.write( " three adults and four children must pay $129.<BR>\n" );
document.write( " two adults and three children must pay $92. <BR>\n" );
document.write( " Find the price of the adults ticket and the price of a child's ticket. <BR>\n" );
document.write( " Adult<BR>\n" );
document.write( " Child </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555866 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=555866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve, we need to set this word problem up as a system of linear equations.  First, let's use the letter A to represent the Adult tickets and C to represent the child tickets.  The problem says that 3 Adults and 4 children must pay 129 dollars.  So,\r<BR>\n" );
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document.write( "3A + 4C = 129\r<BR>\n" );
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document.write( "Next, we are told that 2 Adults and 3 children must pay 92 dollars.  So,\r<BR>\n" );
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document.write( "2A + 3C = 92\r<BR>\n" );
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document.write( "Our system of equations are\r<BR>\n" );
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document.write( "3A + 4C = 129<BR>\n" );
document.write( "2A + 3C = 92\r<BR>\n" );
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document.write( "We need to now solve for either A or C.  Let's choose C.  To solve for C, we need to multiply the first equation by a certain number, so that when we add that first equation to the second equation, our letter A will disappear.  If we multiply equation 1 by -2 and the second equation by 3 and then add them together, our A will go away:\r<BR>\n" );
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document.write( "-2(3A + 4C = 129) -----> -6A - 8C = -258\r<BR>\n" );
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document.write( "3(2A + 3C = 92) -----> 6A + 9C = 276\r<BR>\n" );
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document.write( "Now, let's add these two results together:\r<BR>\n" );
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document.write( "-6A - 8C + 6A + 9C = 276 - 258 -----> C = 18\r<BR>\n" );
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document.write( "Now that we have solved for C, we can replace C in either of our two original equations with 18.  Let's use equation 1:\r<BR>\n" );
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document.write( "3A + 4C = 129 -----> 3A + 4(18) = 129 -----> 3A + 72 = 129\r<BR>\n" );
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document.write( "Next, subtract both sides by 72:\r<BR>\n" );
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document.write( "3A + 72 - 72 = 129 - 72 -----> 3A = 57\r<BR>\n" );
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document.write( "Finally, divide both sides by 3 to solve for A:\r<BR>\n" );
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document.write( "3A/3 = 57/3 -----> A = 19\r<BR>\n" );
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document.write( "Therefore, the price of an Adult ticket is $19 and the price of a Child ticket is $18.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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