Question

Mrs. Bernier is contemplating which chauffeured car service to take to the airport.

Mark’s Miles costs $4 up front and $4 per mile.
Daniela Drives costs $12 plus $2 per mile.
For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?


5 miles and $25


4 miles and $20


20 miles and $4


.25 miles and $5

Answer 1

To find the distance where the two services charge the same fare, we need to set up equations based on the costs of each service.

Let's denote the distance in miles as \( x \).

**Mark’s Miles:**
Cost = \( 4 + 4x \)

**Daniela Drives:**
Cost = \( 12 + 2x \)

We want to find the value of \( x \) where these two costs are equal:

\[
4 + 4x = 12 + 2x
\]

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

1. Subtract \( 2x \) from both sides:

\[
4 + 2x = 12
\]

2. Subtract \( 4 \) from both sides:

\[
2x = 8
\]

3. Divide by \( 2 \):

\[
x = 4
\]

Now, we need to find the total fare when \( x = 4 \).

Using either service to calculate the cost at \( x = 4 \):

Using **Mark’s Miles**:

\[
Cost = 4 + 4(4) = 4 + 16 = 20
\]

Using **Daniela Drives**:

\[
Cost = 12 + 2(4) = 12 + 8 = 20
\]

Both services confirm that the fare is \( 20 \).

Thus, the distance is 4 miles and the total fare is $20.

The correct answer is: **4 miles and $20**.