Arun took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4 plus $4.25 per mile. The total fare was $110.25, not including the tip. How many miles was the taxi ride?

To determine the number of miles Arun's taxi ride was, let's set up an equation based on the information provided.

The fare consists of a pick-up fee of $4 plus $4.25 per mile. Let $ x $ represent the number of miles driven. The total fare is $110.25. The equation to represent this situation is:

\[
4 + 4.25x = 110.25
\]

Now, let's solve for $ x $:

1. Subtract the pick-up fee from the total fare:
   \[
   4.25x = 110.25 - 4
   \]
   \[
   4.25x = 106.25
   \]

2. Divide both sides by 4.25 to find $ x $:
   \[
   x = \frac{106.25}{4.25}
   \]
   \[
   x = 25
   \]

So, the taxi ride was **25 miles** long.

Would you like a detailed explanation or have any further questions?

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Here are some related questions you might find interesting:

1. What would the fare be for a 30-mile ride under the same conditions?
2. How much would the fare be if the pick-up fee was increased to $5?
3. What if the cost per mile was reduced to $3.75 instead—what would the fare be for 25 miles?
4. How would the fare change if Arun had a discount that reduced the total fare by 10%?
5. If Arun decided to tip the driver 15%, what would be the total cost?
6. How would the total fare change if the distance was miscalculated by 2 miles?
7. What would happen to the fare if the pick-up fee was removed entirely?
8. How much would the fare be if the distance was 50 miles?

**Tip:** When solving word problems, it's helpful to identify and write down what each variable represents before setting up the equation. This ensures you correctly model the situation.

Learn how to calculate the taxi fare based on distance and a fixed pick-up fee using a step-by-step solution. This problem involves solving an equation where the fare includes a $4 pick-up fee and $4.25 per mile. Suitable for Grades 7-9 students.

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