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 #842691 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=842691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your 2 equations are:\r<BR>\n" );
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document.write( "30e + 10c = 470<BR>\n" );
document.write( "10e + 30c = 370\r<BR>\n" );
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document.write( "multiply the second equation by 3 and leave the first equation as is to get:\r<BR>\n" );
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document.write( "30e + 10c = 470<BR>\n" );
document.write( "30e + 90c = 1110\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "80c = 640\r<BR>\n" );
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document.write( "solve for c to get:\r<BR>\n" );
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document.write( "c = 640 / 80 = 8\r<BR>\n" );
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document.write( "replace c in the first equation by 8 to get:\r<BR>\n" );
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document.write( "30e + 10 * 8= 470<BR>\n" );
document.write( "subtract 10 * 8 from both sides of the equation to get:<BR>\n" );
document.write( "30e = 470 - 80<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "30e - 390<BR>\n" );
document.write( "solve for e to get:<BR>\n" );
document.write( "e = 390 / 30 = 13\r<BR>\n" );
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document.write( "you have c = 8 and e = 13\r<BR>\n" );
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document.write( "from the first equation, 30e + 10c becomes 30 * 13 + 10 * 8 = 390 + 80 = 470<BR>\n" );
document.write( "from the second equation, 10e + 30c becomes 10 * 13 + 30 * 8 = 130 + 240 = 370\r<BR>\n" );
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document.write( "solution of c = 8 and e = 13 is confirmed to be correct.\r<BR>\n" );
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