Question

A cab service charges customers a base fee and an additional charge per mile of the distance traveled. If x represents the distance traveled, in miles, and y represents the total cost, in dollars, which of the following situations is represented by the table below?

Distance (miles) 5 10 15 20
Total Cost $14.25 $23.50 $32.75 $42
A.
The base fee for hiring a cab is $7, and there is an additional charge of $1.65 per mile.

B.
The base fee for hiring a cab is $5, and there is an additional charge of $9.25 per mile.

C.
The base fee for hiring a cab is $10, and there is an additional charge of $4.25 per mile.

D.
The base fee for hiring a cab is $5, and there is an additional charge of $1.85 per mile.

Answer 1

To determine which situation is represented by the given table, we can use the general formula for the total cost \( y \) in relation to the distance traveled \( x \):

\[
y = \text{base fee} + (\text{charge per mile} \times x)
\]

We'll consider each option and see which one fits the data provided in the table.

1. **Option A: Base fee = $7, Charge per mile = $1.65**
\[
y = 7 + 1.65x
\]
- For \( x = 5 \): \( y = 7 + 1.65(5) = 7 + 8.25 = 15.25 \) (not $14.25)
- This option does not fit.

2. **Option B: Base fee = $5, Charge per mile = $9.25**
\[
y = 5 + 9.25x
\]
- For \( x = 5 \): \( y = 5 + 9.25(5) = 5 + 46.25 = 51.25 \) (not $14.25)
- This option does not fit.

3. **Option C: Base fee = $10, Charge per mile = $4.25**
\[
y = 10 + 4.25x
\]
- For \( x = 5 \): \( y = 10 + 4.25(5) = 10 + 21.25 = 31.25 \) (not $14.25)
- This option does not fit.

4. **Option D: Base fee = $5, Charge per mile = $1.85**
\[
y = 5 + 1.85x
\]
- For \( x = 5 \): \( y = 5 + 1.85(5) = 5 + 9.25 = 14.25 \) (matches)
- For \( x = 10 \): \( y = 5 + 1.85(10) = 5 + 18.5 = 23.50 \) (matches)
- For \( x = 15 \): \( y = 5 + 1.85(15) = 5 + 27.75 = 32.75 \) (matches)
- For \( x = 20 \): \( y = 5 + 1.85(20) = 5 + 37 = 42 \) (matches)

Since Option D matches all entries in the provided table, the correct answer is:

**D. The base fee for hiring a cab is $5, and there is an additional charge of $1.85 per mile.**