Fwam took a taxi from his house to the airport. The taxi company charged a pick-up fee of $3. 80 plus $2. 25 per mile. The total fare was $33. 05, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
The correct answer and explanation is:
Let m represent the number of miles in the taxi ride. The total fare consists of two parts:
- A fixed pick-up fee of $3.80.
- A variable fee that depends on the number of miles traveled, which is $2.25 per mile.
Thus, the total fare can be represented by the equation: 3.80+2.25m=33.053.80 + 2.25m = 33.05
Where:
- 3.80 is the pick-up fee,
- 2.25m is the variable charge based on the miles traveled, and
- 33.05 is the total fare.
To solve for m, follow these steps:
- Subtract the pick-up fee from both sides of the equation:
2.25m=33.05−3.802.25m = 33.05 – 3.80 2.25m=29.252.25m = 29.25
- Divide both sides of the equation by 2.25 to solve for m:
m=29.252.25m = \frac{29.25}{2.25} m=13m = 13
Therefore, the number of miles in the taxi ride is 13 miles.
Explanation:
The equation starts with the fixed cost of the ride and adds the cost per mile, resulting in the total fare. By isolating the variable m, we determine how many miles were traveled. In this case, after subtracting the fixed fee from the total, dividing by the cost per mile gives us the total number of miles.