Rapid Rental Car charges a $40 rental fee, $25 for gas, and $0.65 per mile driven. For the same car, Capital Cars charges $55 for rental and gas and $0.75 per mile.
Part 1 out of 2
For how many miles is the rental cost at both companies the same?
The rental costs at both companies are the same at
miles.

40 + 15 + 0.25x = 45 + 0.35y

55 + 0.25x = 45 + 0.35y The only way you can do this is to assume that x and y are equal

subtract 45 from both sides

55 - 45 + 0.25x = 0.35x

10 + 0.25x = 0.35x Subtract 0.25x from both sides.

10 = 0.35x - 0.25x

10 = 0.1x Divide by 0.1

10/0.1 = x

x = 100 So if each car goes 100 miles, it should turn out to be the same no matter which company gets the rental.

Let's see if that is true.

Cost for the first company = 40 + 15 + 0.25x = 55 + 25 = 80 dollars.

Cost for the second company = 45 + 0.35x = 45 + 35 = 80 dollars.

Conclusion

Both rentals charge the same total amount when each car is driven 100 miles.

The charge is 80 dollars.

Hope this helped! :)