Question

Mr. Tilman took a taxi to Center City. The taxi driver charged a $4 initial fee and $2 for every mile. The final cost of the taxi ride was $28. Which equation models this situation and is solved correctly to determine the number of miles, x, the taxi traveled?

A.
2
+
4
x
=
28
;
x
=
7.5

B.
4
+
2
x
=
28
;
x
=
16

C.
2
+
4
x
=
28
;
x
=
6.5

D.
4
+
2
x
=
28
;
x
=
12

Answer 1

To model the situation described, we start with the initial fee and the cost per mile:

- Initial fee: $4
- Cost per mile: $2
- Total cost: $28

The equation that represents the total cost of the taxi ride can be set up as follows:

\[ 4 + 2x = 28 \]

Where \( x \) is the number of miles traveled.

Now, let's solve the equation:

1. Subtract 4 from both sides:
\[ 2x = 28 - 4 \]
\[ 2x = 24 \]

2. Divide both sides by 2:
\[ x = \frac{24}{2} \]
\[ x = 12 \]

This means the taxi traveled 12 miles.

Looking at the options provided:

- A: \( 2 + 4x = 28; x = 7.5 \) (Incorrect)
- B: \( 4 + 2x = 28; x = 16 \) (Incorrect)
- C: \( 2 + 4x = 28; x = 6.5 \) (Incorrect)
- D: \( 4 + 2x = 28; x = 12 \) (Correct)

Therefore, the correct choice is **D**:

\[ 4 + 2x = 28; \, x = 12 \]