document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=991101>Question 991101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 2000 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611209 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=611209\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first car gets 15 miles per gallon.<BR>\n" );
document.write( "second car gets 40 miles per gallon.<BR>\n" );
document.write( "both cars went a total of 2000 miles for a total gas consumption of 75 gallons.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "miles driven by first car is x.<BR>\n" );
document.write( "miles driven by second car is y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "gallons consumed by first car is x / 15.<BR>\n" );
document.write( "gallons consumed by second car is y / 40.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 2 equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y = 2000<BR>\n" );
document.write( "x/15 + y/40 = 75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use the first equation to solve for y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get y = 2000 - x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace y with 2000 - x in the second equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x/15 + (2000 - x) / 40 = 75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "remove the fractions by multiplying both sides of the equation by 120.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "120 * x / 15 + 120 * (2000 - x) / 40 = 75 * 120\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8 * x + 3 * (2000 - x) = 9000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify further by removing parentheses to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8 * x + 6000 - 3 * x = 9000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 6000 from both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8 * x - 3 * x = 3000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 * x = 3000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 5 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 600\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since y = 2000 - x, this means that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 1400\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first car traveled 600 miles.<BR>\n" );
document.write( "the second car traveled 1400 miles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "600 + 1400 = 2000<BR>\n" );
document.write( "600 / 15 + 1400 / 40 = 40 + 35 = 75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "numbers check out.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is the the first car traveled 600 miles at 15 miles per gallon and the second car traveled 1400 miles at 40 miles per gallon.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );