From the question, we can find the expression for the money Isabella needs to pay, as follows:
[tex]\text{money}=4.5\text{ + (k-1)0.25}[/tex]Where k is the amount of miles. We know that she paid $14.00, so we can find the amount of miles:
[tex]4.5+(k-1)\times0.25=14\rightarrow(k-1)\times0.25=14-4.5\rightarrow k-1=\frac{9.5}{0.25}\rightarrow k=38+1\rightarrow k=39[/tex]So the taxi drove 39 miles.