Arental car agency charges $17 per day plus $.07 per mile to rent a certain car. another agency charges $22 per day plus $.05 per mile to rent the same car. how many miles per day will have to be driven for the cost of a car from the first agency to be greater than the cost of a car from the second agency

Let x represent the number of miles driven. Then the charges from the first agency are ...

... c1 = 17 + 0.07x

and those from the second agency are ...

... c2 = 22 + 0.05x

The first agency's charges will be greater when

... c1 > c2

... 17 + 0.07x > 22 + 0.05x . . . . . . . substitute the above expressions

... 0.02x > 5 . . . . . . . . . . . . . . . . . . . . subtract 17+.05x

... x > 5/0.02

... x > 250

250 miles per day will have to be driven to make the first agency's charges greater.