Translate the phrase 'no more than $25' into a mathematical inequality involving your cost expression and 25. Should you use $<$, $>$, $\le$, or $\ge$?

Once you have your inequality, isolate $m$ by first subtracting 3 from both sides, then dividing both sides by 0.75. Keep track of what the inequality sign is telling you.

After you find the maximum value for $m$, think about whether you should round up or down to get the greatest whole number of miles that still keeps the cost within the budget.

In Desmos, type y = 3 + 0.75x to represent the total cost (in dollars) as a function of miles $x$.

On the next line, type y = 25 to represent Elena's maximum budget as a horizontal line.

Look for the point where the line $y = 3 + 0.75x$ intersects the line $y = 25$. Tap that intersection point and note the $x$-value; this is the maximum number of miles if you spend exactly $25.

Because Elena cannot exceed $25 and the question asks for the greatest whole number of miles, take the largest integer that is less than or equal to the $x$-value you found from the intersection.

Let $m$ be the number of miles Elena travels.

The app charges a flat fee of $3 plus $0.75 per mile, so the cost $C$ in dollars is

Elena wants to spend no more than $25, which means the cost must be less than or equal to 25:

Start with the inequality

Subtract 3 from both sides:

Now divide both sides by $0.75$ to isolate $m$:

Compute the division. Since $0.75 = \tfrac{3}{4}$,

So $m$ must be less than or equal to this value.

The inequality tells us that the number of miles $m$ cannot be greater than $\tfrac{88}{3} \approx 29.33\dots$.

Because Elena cannot travel a fraction of a mile over this limit and the question asks for the greatest whole number of miles, we take the largest integer that is less than or equal to this value.

That greatest whole number of miles is 29.