A rent-a-car charged a fixed daily rate plus a fixed amount per kilometer. A total charge for the first week was $830 with 1250 kilometer on the clock. The second week bill was $710 with 850 kilometer on the clock.Determine the rental charge and the cost per kilometer?

1250x + f = 830

850x + f = 710

or, note that it cost an extra

$120 for 400 km.
That means the mileage rate is $0.30/km

use that to get the fixed rate.

1250x + f = 830

850x + f = 710

To determine the rental charge and the cost per kilometer, we need to set up a system of equations based on the given information.

Let's denote the fixed daily rate as "x" and the fixed amount per kilometer as "y".

From the first week, we have:
Total charge = Fixed daily rate + (Fixed amount per kilometer * Number of kilometers)
$830 = 7x + 1250y

From the second week, we have:
Total charge = Fixed daily rate + (Fixed amount per kilometer * Number of kilometers)
$710 = 7x + 850y

Now, we have a system of equations:
7x + 1250y = $830
7x + 850y = $710

We can solve this system of equations using elimination or substitution method.

Using substitution method:
Rearrange the second equation to solve for x:
7x = $710 - 850y
x = ($710 - 850y) / 7

Substitute the value of x in the first equation:
7(($710 - 850y) / 7) + 1250y = $830

Simplify the equation:
$710 - 850y + 1250y = $830
400y = $120
y = $120 / 400
y = $0.30 per kilometer

Substitute the value of y in either of the original equations to find the value of x:
7x + 1250($0.30) = $830
7x + $375 = $830
7x = $830 - $375
7x = $455
x = $455 / 7
x ≈ $65 per day

Therefore, the rental charge is approximately $65 per day and the cost per kilometer is approximately $0.30.