Question

the allied taxi company charges $2.50 to pick up a passenger and then adds $1.95 per mile. isaac was charged $27.46 to go from one city to another. if x represents the number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did isaac travel, rounded to the nearest tenth?
$2.50x + 1.95 = 27.46$; isaac traveled 11.8 miles.
$1.95x + 2.50 = 27.46$; isaac traveled 15.4 miles.
$2.50x + 1.95 = 27.46$; isaac traveled 10.2 miles.
$1.95x + 2.50 = 27.46$; isaac traveled 12.8 miles.

Explanation:

Step1: Determine the linear equation

The taxi charges a fixed pickup fee of $2.50 and then $1.95 per mile. So the total cost \( y \) (in dollars) for \( x \) miles is given by the equation \( y = 1.95x + 2.50 \). We know the total cost \( y = 27.46 \), so the equation is \( 1.95x + 2.50 = 27.46 \).

Step2: Solve for \( x \)

Subtract 2.50 from both sides:
\( 1.95x = 27.46 - 2.50 \)
\( 1.95x = 24.96 \)

Divide both sides by 1.95:
\( x = \frac{24.96}{1.95} \)
\( x = 12.8 \)

Answer:

\( 1.95x + 2.50 = 27.46 \); Isaac traveled 12.8 miles.