Questions: A moving truck rental company charges 23.95 to rent a truck, plus 0.87 per mile. Suppose the function C(d) gives the total cost of renting the truck for one day if you drive 23 miles. Give the formula for C(d). Make sure to give the complete formula as an equation. Give the total rental cost if you drive the truck 23 miles. Give the function notation in the first box, the answer in the second box, and choose the correct units from the third box. Suppose you have 95 budgeted to move. What is the furthest distance you can drive the truck? Round your answer to the nearest whole number and choose the correct units.

Solution Steps

The total cost \( C(d) \) of renting the truck for one day, where \( d \) is the distance driven in miles, is given by the equation: \[ C(d) = 23.95 + 0.87d \]

To find the total rental cost when driving 23 miles, substitute \( d = 23 \) into the cost function: \[ C(23) = 23.95 + 0.87 \times 23 \] Calculating this gives: \[ C(23) = 23.95 + 20.01 = 43.96 \]

To find the maximum distance \( d \) that can be driven within a budget of $95, set up the inequality: \[ 23.95 + 0.87d \leq 95 \] Solving for \( d \): \[ 0.87d \leq 95 - 23.95 \] \[ 0.87d \leq 71.05 \] \[ d \leq \frac{71.05}{0.87} \] Calculating this gives: \[ d \leq 81.66666666666666 \] Rounding to the nearest whole number, the maximum distance is: \[ d = 82 \]

Final Answer