document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165931>Question 1165931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 35 gallons of gas. The two cars drove a combined total of 1650 miles, and the sum of their fuel efficiencies was 50 miles per gallon. What were the fuel efficiencies of each of the cars that week?<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 #790426 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=790426\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> miles divided by gallons = miles per gallon.\r<BR>\n" );
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document.write( "let x = the miles driven by the car that consumed 30 gallons of gas.\r<BR>\n" );
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document.write( "let y = the miles driven by the car that consumed 35 gallons of gax.\r<BR>\n" );
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document.write( "total miles driven is 1650.\r<BR>\n" );
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document.write( "your two equations are:\r<BR>\n" );
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document.write( "x + y = 1650<BR>\n" );
document.write( "x/30 + y/35 = 50\r<BR>\n" );
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document.write( "the first equation tells you the total miles driven.<BR>\n" );
document.write( "the second equation tells you the total miles per gallon consumed.\r<BR>\n" );
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document.write( "multiply both sides of the first eqution by 30 and multiply both sides of the second equation by 30 * 35 = 1050 to get:\r<BR>\n" );
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document.write( "30x + 30y = 49500<BR>\n" );
document.write( "35x + 30y = 52500\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:<BR>\n" );
document.write( "5x = 3000\r<BR>\n" );
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document.write( "solve for x to get:<BR>\n" );
document.write( "x = 600\r<BR>\n" );
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document.write( "since x + y = 1650, this makes y = 1050\r<BR>\n" );
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document.write( "you have x = 600 and y = 1050\r<BR>\n" );
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document.write( "check to see if these values make your original equations true.\r<BR>\n" );
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document.write( "your original equations are:<BR>\n" );
document.write( "x + y = 1650<BR>\n" );
document.write( "x/30 + y/35 = 50\r<BR>\n" );
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document.write( "these equations become:<BR>\n" );
document.write( "600 + 1050 = 1650 which is true.<BR>\n" );
document.write( "600/30 + 1050/35 = 50 which is also true.\r<BR>\n" );
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document.write( "miles / gallons = miles per gallon.\r<BR>\n" );
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document.write( "600/30 = 20 miles per gallon for the car that consumed 30 gallons.<BR>\n" );
document.write( "1050/35 = 30 miles per gallon for the car that consumed 35 gallons.\r<BR>\n" );
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document.write( "those are your solutions.\r<BR>\n" );
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document.write( "to double check:\r<BR>\n" );
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document.write( "miles / miles per gallon = gallons consumed.\r<BR>\n" );
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document.write( "600/20 = 30 gallons<BR>\n" );
document.write( "1050 / 30 = 35 gallons\r<BR>\n" );
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document.write( "it all checks out.\r<BR>\n" );
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document.write( "your solution is that the first car had a fuel efficiency of 20 miles per gallon and the second car has a fuel efficienty of 30 miles per gallon. </SPAN>\n" );
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