Sydney took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.60 plus $1.75 per mile. The total fare was $20.85, 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 the taxi ride, we can set up the equation based on the given information.

The total fare consists of a pick-up fee and a charge per mile. The pick-up fee is $1.60, and the charge is $1.75 per mile. Therefore, the total fare can be expressed with the equation:

\[ \text{Total Fare} = \text{Pick-up Fee} + (\text{Cost per Mile} \times \text{Number of Miles}) \]

Substituting the known values into the equation:

\[ 20.85 = 1.60 + 1.75x \]

Now, we will solve for \( x \):

1. Subtract the pick-up fee from both sides:

\[ 20.85 - 1.60 = 1.75x \]

\[ 19.25 = 1.75x \]

2. Divide both sides by 1.75 to isolate \( x \):

\[ x = \frac{19.25}{1.75} \]

3. Perform the division:

\[ x = 11 \]

Thus, the number of miles in the taxi ride is \( \boxed{11} \).