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?
○ 1.95x + 2.50 = 27.46; isaac traveled 15.4 miles.
○ 1.95x + 2.50 = 27.46; isaac traveled 12.8 miles.
○ 2.50x + 1.95 = 27.46; isaac traveled 11.8 miles.
○ 2.50x + 1.95 = 27.46; isaac traveled 10.2 miles.

Explanation:

Step1: Define cost components

Fixed pick-up fee: $\$2.50$, variable cost: $\$1.95$ per mile. Total cost = fixed cost + variable cost.

Step2: Set up linear equation

Let $x$ = miles driven. Equation: $1.95x + 2.50 = 27.46$

Step3: Isolate variable term

Subtract 2.50 from both sides:
$1.95x = 27.46 - 2.50$
$1.95x = 24.96$

Step4: Solve for x

Divide by 1.95:
$x = \frac{24.96}{1.95} = 12.8$

Answer:

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