We want to find how many miles Jodi traveled if her ride costed $12.50. We also know that a taxi ride has an initial fee of $3.75 plus $1.25 for every 1/2 mile traveled.
This means that for every mile, the fee will be:
[tex]2(1.25)=2.50[/tex]And the expression for the cost on terms of the miles traveled will be:
[tex]\begin{gathered} 3.75+2.50x \\ \text{where }x\text{ represents the number of miles traveled } \end{gathered}[/tex]As we know that Jodi spent $12.50 on a ride, we equal the value to the above expression:
[tex]3.75+2.50x=12.50[/tex]And we solve for x, as we want to know the number of miles:
[tex]\begin{gathered} 2.50x=12.50-3.75 \\ 2.50x=8.75 \\ x=\frac{8.75}{2.50}=3.5 \end{gathered}[/tex]This means that the number of miles that Jodi traveled was 3 and a half.