document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205707>Question 1205707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When London spent 30 minutes on the elliptical trainer and then did circuit training for 10 minutes, her fitness app said she burned 470 calories. When she spent 10 minutes on the elliptical trainer and 30 minutes circuit training she burned 370 calories. Solve the system:\r<BR>\n" );
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document.write( "{ (30 e + 10 c = 470), (10 e + 30 c = 370) :}\r<BR>\n" );
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document.write( "for e , the number of calories she burned for each minute on the elliptical trainer, and c , the number of calories she burned for each minute of circuit training.\r<BR>\n" );
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document.write( "     e = \r<BR>\n" );
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document.write( "     c = <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 #842694 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=842694\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The problem clearly involves solving a system of two linear equations; there are always a large number of choices of how to solve them.<br><BR>\n" );
document.write( "e = calories burned per minute on elliptical trainer<BR>\n" );
document.write( "c = calories burned per minute on circuit training<br><BR>\n" );
document.write( "30e + 10c = 470<BR>\n" );
document.write( "10e + 30c = 370<br><BR>\n" );
document.write( "With those two equations, my clear choice for a solution path is the following.<br><BR>\n" );
document.write( "Add the two starting equations and simplify:<BR>\n" );
document.write( "40e + 40c = 840<BR>\n" );
document.write( "10e + 10c = 210<br><BR>\n" );
document.write( "Compare that equation to each of the starting equations:<br><BR>\n" );
document.write( "20e = 260<BR>\n" );
document.write( "20c = 160<br><BR>\n" );
document.write( "Solve:<BR>\n" );
document.write( "e = 13<BR>\n" );
document.write( "c = 8<br><BR>\n" );
document.write( "ANSWER: 13 calories per minute on the elliptical trainer; 8 per minute on the circuit training<br><BR>\n" );
document.write( "Obviously this solution method is only useful because of the exact numbers used... but it is a worthwhile thing to look out for in a problem like this.<br><BR>\n" );
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