rapid rental car company charges a $40 rental fee, $15 for gas, and 0.25 per mile driven. for the same car, capitol cars charges $45 for rental and gas and 0.35 per mile. find the number of miles for which the companies will charge the same. then find that charge.

Equation

40 + 15 + 0.25x = 45 + 0.35y

Solution

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.