Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $111.00 for 3 days and 300 miles, while Mary was charged $198.00 for 5 days and 600 miles. What does Best Rentals charge per day and per mile?
Eq1: 3x + 300y = 111
Eq2: 5x + 600y = 198
Multiply Eq1 by -5 and Eq2 by 3 :
-15x - 1500y = -555
+15x + 1800y = +594
Sum: 300y = 39
Y = $0.13 per mile.
In Eq1, replace Y with 0.13 and solve for X:
3x + 300*0.13 = 111
3x = 111 - 39 = 72
X = $24 per day.
To determine the daily fee and the mileage fee, we can set up a system of equations based on the information given.
Let's assume that the daily fee is represented by "D" and the mileage fee is represented by "M".
From the first scenario, we know that Barney was charged $111.00 for 3 days and 300 miles. This can be represented as the equation:
3D + 300M = 111.00
Similarly, from the second scenario, we know that Mary was charged $198.00 for 5 days and 600 miles. This can be represented as the equation:
5D + 600M = 198.00
We now have a system of two equations with two variables. We can solve this system to find the values of D (daily fee) and M (mileage fee).
To find these values, we can use substitution or elimination method. Let's use the elimination method:
Multiply the first equation by 5 and the second equation by 3 to make the coefficients of D in both equations equal:
15D + 1500M = 555.00 (Multiplying the first equation by 5)
15D + 1800M = 594.00 (Multiplying the second equation by 3)
Now, subtract the first equation from the second equation to eliminate D:
(15D + 1800M) - (15D + 1500M) = 594.00 - 555.00
This simplifies to:
300M = 39.00
Divide both sides of the equation by 300:
M = 39.00 / 300
M = 0.13
Now that we know the mileage fee is $0.13 per mile, we can substitute this value back into one of the original equations to find the daily fee (D). Let's use the first equation:
3D + 300M = 111.00
Substituting the value of M:
3D + 300(0.13) = 111.00
Simplifying:
3D + 39.00 = 111.00
Subtract 39.00 from both sides:
3D = 72.00
Divide both sides by 3:
D = 72.00 / 3
D = 24.00
Therefore, Best Rentals charges a daily fee of $24.00 and a mileage fee of $0.13 per mile.