Questions: A rental truck costs 76.45 for a day plus 94 cents per mile. (a) If x is the number of miles driven, write an expression for the total cost C, in dollars, of renting the truck for a day. C= (b) Find the total cost of the rental if it was driven 124 miles.

A rental truck costs 76.45 for a day plus 94 cents per mile.
(a) If x is the number of miles driven, write an expression for the total cost C, in dollars, of renting the truck for a day.
C=

(b) Find the total cost of the rental if it was driven 124 miles.

Transcript text: A rental truck costs $\$ 76.45$ for a day plus 94 \& per mile. (a) If $x$ is the number of miles driven, write an expression for the total cost $C$, in dollars, of renting the truck for a day. \[ C= \] (b) Find the total cost of the rental if it was driven 124 miles.

Solution

Solution Steps

Solution Approach

(a) To find the expression for the total cost $ C $ of renting the truck, we need to account for the fixed daily cost and the variable cost per mile. The fixed cost is \$76.45, and the variable cost is 94 cents per mile. Therefore, the expression for the total cost is the sum of the fixed cost and the product of the number of miles driven $ x $ and the cost per mile.

(b) To find the total cost when the truck is driven for 124 miles, substitute $ x = 124 $ into the expression derived in part (a) and calculate the result.

Step 1: Define the Expression for Total Cost

To find the total cost $ C $ of renting the truck for a day, we need to consider both the fixed daily cost and the variable cost per mile. The fixed cost is \$76.45, and the variable cost is 94 cents per mile. Therefore, the expression for the total cost is:

\[ C = 76.45 + 0.94x \]

where $ x $ is the number of miles driven.

Step 2: Calculate the Total Cost for 124 Miles

To find the total cost when the truck is driven for 124 miles, substitute $ x = 124 $ into the expression for $ C $:

\[ C = 76.45 + 0.94 \times 124 \]

Calculate the result:

\[ C = 76.45 + 116.56 = 193.01 \]