Question

Lydia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.10 plus $2.50 per mile. The total fare was $36.60, not including the tip. Write and solve an equation which can be used to determine xx, the number of miles in the taxi ride.

Answer 1

To determine the number of miles \( x \) in Lydia's taxi ride, we can set up an equation based on the information given.

The total cost of the taxi fare can be expressed as:

\[
\text{total cost} = \text{pick-up fee} + (\text{cost per mile} \times \text{number of miles})
\]

From the problem, we know:
- The pick-up fee is \( 4.10 \) dollars.
- The cost per mile is \( 2.50 \) dollars.
- The total fare is \( 36.60 \) dollars.

We can write the equation as:

\[
36.60 = 4.10 + 2.50x
\]

To find \( x \), we will first isolate the term involving \( x \). Subtract \( 4.10 \) from both sides:

\[
36.60 - 4.10 = 2.50x
\]

Calculating the left side:

\[
32.50 = 2.50x
\]

Now, divide both sides by \( 2.50 \) to solve for \( x \):

\[
x = \frac{32.50}{2.50}
\]

Calculating this gives:

\[
x = 13
\]

Thus, the number of miles in the taxi ride is \( \boxed{13} \).