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.