document.write( "Question 1143680: Discount Rental Cars charges a daily fee plus a mileage fee for renting its cars. Barney was charged $145.00 for 3 days and 310 miles, while Mary was charged $250.00 for 5 days and 600 miles. What does Discount Rental Cars charge per day and per mile?please show me the steps that you did to get to the answer. \n" ); document.write( "

Algebra.Com's Answer #764559 by ikleyn(52864) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Let \"d\" be the charge per day and \"m\" be the charge per mile.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then from the condition, you have these two equations\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    3d + 310m = 145.00  dollars    (1)   (how much Barney was charged)\r\n" );
document.write( "\r\n" );
document.write( "    5d + 600m = 250.00  dollars    (2)   (how much Mary   was charged)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At this point, the setup is just completed.\r\n" );
document.write( "\r\n" );
document.write( "This part of the solution is rather simple.\r\n" );
document.write( "\r\n" );
document.write( "It is quite obvious and usually does not create any difficulties.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus you have this system of equations, and now your task is to solve it.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There are different methods of solution : the Substitution method;  the Elimination method and the Cramer's rule (using determinants).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I will use the Elimination method. \r\n" );
document.write( "For It, I multiply equation (1) by 5 (both sides) and multiply equation (2) by 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You will get modified equivalent system\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    15d + 1550m = 725.00      (3)  \r\n" );
document.write( "\r\n" );
document.write( "    15d + 1800m = 750.00      (4)   (how much Barney was charged)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice the the coefficients at \"d\" are equal in both equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next step, subtract equation (3) from equation (4).  The terms \"15d\" in both equations will cancel each other, \r\n" );
document.write( "and you will get a single equation for one unknown \"m\" :\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    1800m - 1550m = 750.00 - 725,    or\r\n" );
document.write( "\r\n" );
document.write( "    250m          = 25,\r\n" );
document.write( "\r\n" );
document.write( "       m          = 25/250 = 0.1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus you just found the unknown \"m\" : it is 0.1  (dollar per mile).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To get the second unknown, simply substitute this value m= 0.1 into either of the two original equations.\r\n" );
document.write( "\r\n" );
document.write( "I will substitute into equation (1). Then you get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    3d + 310*0.1 = 145,\r\n" );
document.write( "\r\n" );
document.write( "    2d + 31      = 145,\r\n" );
document.write( "\r\n" );
document.write( "    3d           = 145 - 31 = 114,\r\n" );
document.write( "\r\n" );
document.write( "     d           = 114/3 = 38.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The company charges  38 dollars per day and 0.1 dollars (= 10 cents) per mile.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "The problem is just solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The last step is to check the answer.
\n" ); document.write( "For it, substitute the found values into the original equations.
\n" ); document.write( "I expect that you do it on your own.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The solution is completed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you are a novice in solving word problems on two equations in two unknown, look into my lessons in this site\r
\n" ); document.write( "\n" ); document.write( "    - Oranges and grapefruits \r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on tickets \r
\n" ); document.write( "\n" ); document.write( "    - Three methods for solving standard (typical) problems on tickets\r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on shares \r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on investment\r
\n" ); document.write( "\n" ); document.write( "    - Two mechanics work on a car \r
\n" ); document.write( "\n" ); document.write( "    - The Robinson family and the Sanders family each used their sprinklers last summer\r
\n" ); document.write( "\n" ); document.write( "    - Roses and vilolets \r
\n" ); document.write( "\n" ); document.write( "    - Counting calories and grams of fat in combined food\r
\n" ); document.write( "\n" ); document.write( "    - A theater group made appearances in two cities\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO algebreze and solve this problem on 2 equations in 2 unknowns \r
\n" ); document.write( "\n" ); document.write( "    - One unusual problem to solve using system of two equations \r
\n" ); document.write( "\n" ); document.write( "    - Solving mentally word problems on two equations in two unknowns \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on solving systems of two linear equations in two unknowns\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You will find there many typical word problems with detailed solutions, clearly explained and demonstrating different solution methods.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook, problems book with solutions, guide, tutorials and (free of charge) home teacher.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Systems of two linear equations in two unknowns\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );