document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196509>Question 1196509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been struggling with a word problem.  The problem is \"Best rentals charges a daily fee plus a milage fee for renting its cars.  Mateo was charged $111.00 for 3 days and 300 miles, while Dara was charged $207.00 for 5 days and 600 miles.  What does Best Rentals charge per day and per mile?\"  \r<BR>\n" );
document.write( "\n" );
document.write( "I have tried to come up with an equation for this, but I've only managed to confuse myself.  I have tried putting the time in as \"x\" and miles in as \"y\" and putting them equal to the total rental charge, then solving for \"x\" and \"y\".  Obviously I'm not solving anything with that arrangement.  I have tried making a \"tic tac toe\" table with the given data, should I be adding all my data up and using that to make a bigger equation.  I am just confused with how to set this up.  Any help is greatly appreciated, thank you.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829366 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=829366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I appreciate you showing your work and thought process, rather than just copy/pasting the problem only.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = cost per day<BR>\n" );
document.write( "y = cost per mile<BR>\n" );
document.write( "Both costs are in dollars\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's list the given facts<BR>\n" );
document.write( "[1] Mateo was charged $111.00 for 3 days and 300 miles<BR>\n" );
document.write( "[2] Dara was charged $207.00 for 5 days and 600 miles\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Fact [1] gives us the equation<BR>\n" );
document.write( "3x+300y = 111<BR>\n" );
document.write( "since<BR>\n" );
document.write( "3x = 3 times x = cost for the 3 days<BR>\n" );
document.write( "300y = cost for the 300 miles<BR>\n" );
document.write( "3x+300y = total cost\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Fact [2] yields the equation 5x+600y = 207 through similar reasoning.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's our system of equations<BR>\n" );
document.write( "3x+300y = 111<BR>\n" );
document.write( "5x+600y = 207\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's double the first equation to go from 3x+300y=111 to 6x+600y = 222\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We arrive at this equivalent system of equations<BR>\n" );
document.write( "6x+600y = 222<BR>\n" );
document.write( "5x+600y = 207\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice the 600y terms matching up. This allows us to cancel out the y terms if we subtract straight down<BR>\n" );
document.write( "The x terms combine to 6x-5x = 1x = x<BR>\n" );
document.write( "The right hand sides combine to 222-207 = 15\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, x = 15\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then we can determine y<BR>\n" );
document.write( "3x+300y = 111<BR>\n" );
document.write( "3*15+300y = 111<BR>\n" );
document.write( "45+300y = 111<BR>\n" );
document.write( "300y = 111-45<BR>\n" );
document.write( "300y = 66<BR>\n" );
document.write( "y = 66/300<BR>\n" );
document.write( "y = 0.22<BR>\n" );
document.write( "You could use other equations previously mentioned involving x and y. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We found that: x = 15 and y = 0.22<BR>\n" );
document.write( "Therefore, it costs $15 per day and $0.22 per mile (aka 22 cents per mile).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "Check:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Mateo:<BR>\n" );
document.write( "1 day = 15 dollars <BR>\n" );
document.write( "3 days = 15*3 = 45 dollars so far<BR>\n" );
document.write( "1 mile = 0.22 dollars<BR>\n" );
document.write( "300 miles = 300*0.22 = 66 dollars added on<BR>\n" );
document.write( "45+66 = 111 dollars total for Mateo\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Or we could say<BR>\n" );
document.write( "3x+300y = 111<BR>\n" );
document.write( "3*15+300*0.22 = 111<BR>\n" );
document.write( "45+66 = 111<BR>\n" );
document.write( "111 = 111<BR>\n" );
document.write( "which confirms Mateo's equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's follow a similar idea for Dara<BR>\n" );
document.write( "5x+600y = 207<BR>\n" );
document.write( "5*15+600*0.22 = 207<BR>\n" );
document.write( "75+132 = 207<BR>\n" );
document.write( "207 = 207<BR>\n" );
document.write( "Her equation is confirmed as well.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Both equations are true for (x,y) = (15, 0.22)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=red>Answers:</font><BR>\n" );
document.write( "$15 per day<BR>\n" );
document.write( "$0.22 per mile (aka 22 cents per mile)<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );