SOLUTION: Twice last​ month, Judy Carter rented a car in​ Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily​ fee, plus

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Question 1136671: Twice last​ month, Judy Carter rented a car in​ Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily​ fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4​ days, she drove 390 ​miles, and the rental cost her ​$260.50. On her second business trip she drove 190 miles in 3​ days, and paid ​$159.50 for the rental. Find the daily fee and the mileage charge.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
Let x be daily fee and y be additional charge per mile.

Then from the condition we have this system of 2 equations in 2 unknowns



    4x + 390y = 260.50  dollars    (1)

    3x + 190y = 159.50  dollars    (2)



Now I apply the determinant method (the Cramer's rule) :


    1)  d = determinant of the coefficient matrix = 4*190 - 3*390 = -410;


    2)  x =  = 31;


    3)  y =  = 0.35.


ANSWER.  Daily fee is $31;  Mileage charge is $0.35 per mile.

Solved.

------------------

On the Determinants' method for solving the systems of two linear equations in two unknowns see the lessons
    - Solution of the linear system of two equations in two unknowns using determinant
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



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