1. Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $123.00 for 3 days and 300 miles, while Mary was charged $216.00 for 5 days and 600 miles. What does Best Rental charge per day, for mileage?

break it down line by line to set up your equations.

using d for daily charge and m for mileage charge,

Barney: 3d + 300m = 123
Mary: 5d + 600m = 216

Subtract M from 2*B:

d = 30
so, m = .11

check: 3*30 + 300*.11 = 90+33 = 123
5*30 + 600*.11 = 150+66 = 216

To find out what Best Rentals charges per day and for mileage, we can set up a system of equations.

Let's denote the daily fee as "D" and the mileage fee as "M."

Based on the given information, we can create two equations:

1) $123.00 = 3D + 300M
2) $216.00 = 5D + 600M

We can solve this system of equations to find the values of D and M.

To eliminate one variable, we can multiply equation 1 by 2 and equation 2 by 3:

1) 2($123.00) = 2(3D + 300M) => $246.00 = 6D + 600M
2) 3($216.00) = 3(5D + 600M) => $648.00 = 15D + 1800M

Subtract equation 1 from equation 2:

($648.00 - $246.00) = (15D + 1800M) - (6D + 600M)
$402.00 = 9D + 1200M

Now we have a new equation:

3) $402.00 = 9D + 1200M

We can notice that equation 3 is just three times equation 1. This suggests that equation 1 was the correct equation to start with, so we can conclude that Best Rentals charges a daily fee of $3 per day.

Now we can substitute this value into equation 1 to find the mileage fee:

$123.00 = 3D + 300M
$123.00 = 3($3.00) + 300M
$123.00 = $9.00 + 300M

To isolate M, we subtract $9.00 from both sides:

$123.00 - $9.00 = 300M
$114.00 = 300M

Finally, we divide both sides by 300 to find the mileage fee:

M = $114.00 / 300
M ≈ $0.38

Therefore, Best Rentals charges $3.00 per day for rentals and approximately $0.38 per mile.

To find the daily fee and mileage fee, we will set up a system of equations using the given information.

Let's assume the daily fee is represented by 'd' and the mileage fee is represented by 'm'.

Based on the given information:

For Barney:
3d + 300m = $123.00

For Mary:
5d + 600m = $216.00

We can now solve this system of equations using any method (substitution, elimination, etc.).

First, let's solve for 'd' in terms of 'm' by isolating 'd' in the first equation:

3d = $123.00 - 300m
d = ($123.00 - 300m)/3

Now, substitute this value of 'd' in the second equation:

5(($123.00 - 300m)/3) + 600m = $216.00

Simplify the equation:

(5/3)($123.00 - 300m) + 600m = $216.00
(5/3)*$123.00 - (5/3)*300m + 600m = $216.00
$205.00 - 500m + 600m = $216.00

Combine like terms:

100m = $11.00

Divide both sides of the equation by 100:

m = $0.11

Therefore, Best Rental charges $0.11 per mile for mileage.