document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212168>Question 212168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The engines on the Great Eastern Railway all have six axles and the cars (tankers and hoppers) all have four axles. If a recent train consisted of 43 units and had 178 axles, how many engines and how many cars were in the train? Note:  an axle is a rod that holds a pair of wheels in place.\r<BR>\n" );
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document.write( "When it came time to discuss the problem, students were first asked to simply tell the strategy they used to approach it. As a teacher, try to put yourself in the place of the students and work the problem in the manner that you anticipate the student has worked it.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160224 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=160224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> engines have 6 axles each.<BR>\n" );
document.write( "cars have 4 axles each.<BR>\n" );
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document.write( "train consists of 43 units and 178 axles.<BR>\n" );
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document.write( "let x = number of engines and let y = number of cars (tankers and hoppers).<BR>\n" );
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document.write( "you have:<BR>\n" );
document.write( "x + y = 43<BR>\n" );
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document.write( "that would be one equation.<BR>\n" );
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document.write( "each engine has 6 axles and each car has 4 axles.<BR>\n" );
document.write( "6x + 4y = 178<BR>\n" );
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document.write( "you cannot solve these equations separately but you can solve them jointly.<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.<BR>\n" );
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document.write( "the equations are:<BR>\n" );
document.write( "x + y = 43<BR>\n" );
document.write( "6x + 4y = 178<BR>\n" );
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document.write( "you can solve these by substitution.<BR>\n" );
document.write( "you solve for one of the variables in one of the equations and then you replace that variable in the other equation.<BR>\n" );
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document.write( "we'll solve for y in the first equation.<BR>\n" );
document.write( "we get y = 43 - x<BR>\n" );
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document.write( "we'll replace y in the second equation with 43 - x<BR>\n" );
document.write( "we get:<BR>\n" );
document.write( "6x + 4 * (43-x) = 178<BR>\n" );
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document.write( "we expand this equation to get:<BR>\n" );
document.write( "6x + 4*43 - 4x = 178<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "6x + 172 - 4x = 178<BR>\n" );
document.write( "we combine like terms to get:<BR>\n" );
document.write( "2x + 172 = 178<BR>\n" );
document.write( "we subtract 172 from both sides of equation to get:<BR>\n" );
document.write( "2x = 178 - 172 = 6<BR>\n" );
document.write( "we divide both sides by 2 to get:<BR>\n" );
document.write( "x = 3<BR>\n" );
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document.write( "the train has 3 engines and 40 cars.<BR>\n" );
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document.write( "3*6 = 18<BR>\n" );
document.write( "40*4 = 160<BR>\n" );
document.write( "160 + 18 = 178<BR>\n" );
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document.write( "x = 3 and y = 40 looks good.<BR>\n" );
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document.write( "3 + 40 = 43<BR>\n" );
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