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 with an equation, we start with the initial fee and the cost per mile. The taxi driver charges a $4 initial fee and $2 for every mile traveled.

1. Let \( x \) be the number of miles traveled.
2. The initial fee is $4.
3. The cost for \( x \) miles is \( 2x \).
4. The total cost for the ride is given as $28.

Thus, the equation that models this situation is:

\[
4 + 2x = 28
\]

Now, to solve for \( x \):

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

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

So, the correct equation that models this situation is \( 4 + 2x = 28 \), and the correct value for \( x \) is 12.

Therefore, the correct choice is:

**D. \( 4 + 2x = 28; \, x = 12 \)**