SOLUTION: Solve by elimination method. Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $120 for 3 days and 300 miles, while Mary was charged $

Algebra ->  Equations -> SOLUTION: Solve by elimination method. Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $120 for 3 days and 300 miles, while Mary was charged $      Log On


   

Question 1161268: Solve by elimination method.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $120 for 3 days and 300 miles, while Mary was charged $210 for 5 days and 600 miles. What does Best Rental charge per day and per mile?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
d= daily fee in $ per day
m=mileage fee in $ per mile

For Barney, the equation is
3d%2B300m=120.
Multiplying both sides of that equation times 2 we get
6d%2B600m=240 .

For Mary, the equation is
5d%2B600m=210 .
Subtracting from the previous equation
(or multiplying times -1 and combining equations we get
6d%2B600m-5d-600m=240-210 ,
which simplifies to
highlight%28d=30%29 .
We have "eliminated" variable m to find the value for d .
That was quite easy.
It would have been a lot more cumbersome to try the other way around.

Hopefully the elimination requirement is considered satisfied,
and we would be allowed to substitute into 3d%2B300m=120.
the value found for d to get
3%2A30%2B300m=120 ,
which simplifies to
90%2B300m=120
and solve going through
300m=120-90 and 300m=30
to get to
m=30%2F300 and highlight%28m=0.1%29 .
So, the daily charge is highlight%28%22%2430%22%29 per day, and
the mileage charge is highlight%28%22%240.10%22%29 per mile.