Answer
More than $100$ miles must be driven in a day.
Work Step by Step
Let the number of miles per day be $x$.
Basic Rental charges is $\$50$ a day plus $\$0.20$ per mile.
Continental charges is $\$20$ a day plus $\$0.50$ per mile.
In the mathematical form.
Basic Rental charges $=50+0.20x$.
Continental charges is $=20+0.50x$.
For the Basic Rental to be a better deal the inequality is.
Continental charges $>$ Basic Rental charges.
The inequality is
$\Rightarrow 20+0.50x>50+0.20x$.
Add $-20-0.20x$ to both sides.
$\Rightarrow 20+0.50x-20-0.20x>50+0.20x-20-0.20x$.
Simplify.
$\Rightarrow 0.30x>30$.
Divide both sides by $0.30$.
$\Rightarrow \frac{0.30x}{0.30}>\frac{30}{030}$.
Simplify.
$\Rightarrow x>100$.
Hence, more than $100$ miles must be driven in a day.
