Question

You want to rent a car for the day.Prestige car rentals charges $47 plus $0.07 per mile to rent a midsize vehicle . Gateway Auto changes a $35 fee plus $0.12 per mile for the same car. For what number of miles will both companies charge the same price?

Answer 1

Answer:

240 miles

Step-by-step explanation:

Given that:

Charges offered by Prestige car rentals for renting a midsize vehicle:

Fixed charges = $47

Per mile charges for renting a midsize vehicle = $0.07

Charges offered by Gateway Auto for renting a midsize vehicle:

Fixed charges = $35

Per mile charges for renting a midsize vehicle = $0.12

To find:

Number of miles for which both the companies charge the same price?

Solution:

Let the number of miles for which both the companies will charge the same price = $x$ miles

Charges for one mile by Prestige car rentals = $0.07

Charges for $x$ miles by Prestige car rentals = $0.07$x$

Total charges by Prestige Car rentals = $47 + $0.07$x$

Charges for one mile by Gateway Auto = $0.12

Charges for $x$ miles by Gateway Auto = $0.12$x$

Total charges by Gateway Auto = $35 + $0.12$x$

As per question statement, the charges are same:

$\ 47 + \ 0.07x = \ 35 + \ 0.12x\\\Rightarrow 12=0.05x\\\Rightarrow x=\dfrac{1200}{5}\\\Rightarrow \bold{x=240\ miles}$