Car rental agency A charges $50 per day plus 10 cents per mile driven. Agency B charges $20 per day plus 30 cents per mile driven. For a one-day rental it is cheaper to rent from agency A if you drive more than?

50 + .10m = 20 + .30m

Solve for m.

To determine when it is cheaper to rent from agency A, we need to find the mileage threshold at which the total cost of renting from agency A becomes lower than the total cost of renting from agency B.

Let's denote:
- X as the number of miles driven.
- C(A) as the total cost of renting from agency A.
- C(B) as the total cost of renting from agency B.

For agency A, the total cost can be calculated as:
C(A) = 50 (base rental cost) + 0.10 (cost per mile) * X (miles driven)

For agency B, the total cost can be calculated as:
C(B) = 20 (base rental cost) + 0.30 (cost per mile) * X (miles driven)

Now, let's set up an equation to find when the total cost of renting from agency A becomes lower than the total cost of renting from agency B:
50 + 0.10X < 20 + 0.30X

Simplifying the equation:
0.10X - 0.30X < 20 - 50
-0.20X < -30
X > -30 / -0.20
X > 150

Therefore, if you drive more than 150 miles, it is cheaper to rent from agency A for a one-day rental.