#### Explanation:

Let the prices be increased in steps of $10$ cents. If prices are increased by $x$ such steps, the price becomes $\left(1.25 + \frac{x}{10}\right)$ per ride.

But number of passengers will go down by $500 x$ and revenue will be

$\left(1.25 + \frac{x}{10}\right) \left(10000 - 500 x\right)$ or

$\left(125 + 10 x\right) \left(100 - 5 x\right)$ - dividing second binomial by $100$ and multiplying first by $100$. This is equivalent to

$12500 + 1000 x - 625 x - 50 {x}^{2}$ or

$12500 + 375 x - 50 {x}^{2}$

Now we should have an extrema where first derivative is zero and as it is $375 - 100 x = 0$ or $x = 3.75$.

Note that second derivative is $- 100$ and as such it is a maxima.

Hence, profit would maximize at $1.25 + 0.375 = 1.625$ per passenger at which maximum revenue would be 1.625(10000-500×3.75)=13203.125.