Question: A truck can be rented from Company A for $100 a day plus $0.40 per mile. Company B charges $30 a…

A truck can be rented from Company A for $100 a day plus $0.40 per mile. Company B charges $30 a day plus $0.90 per mile to rent the same truck. How many miles must be driven in a day to make the rental cost for Company A a better deal than Company B’s?

For Company A to have a better deal, the truck must be driven more than \(\boxed{\phantom{000}}\) miles per day.

Solution

Let’s determine the number of miles that must be driven for Company A to be the better deal compared to Company B. First, define the variables: - Let \( x \) be the number of miles driven in a day. Set up the cost equations for both companies: \[ \text{Cost}{A} = 100 + 0.40x \] \[ \text{Cost}{B} = 30 + 0.90x \] To find when Company A is cheaper than Company B: \[ 100 + 0.40x < 30 + 0.90x \] Subtract \( 0.40x \) from both sides: \[ 100 < 30 + 0.50x \] Subtract 30 from both sides: \[ 70 < 0.50x \] Divide both sides by 0.50: \[ 140 < x \] Therefore, the number of miles that must be driven for Company A to be the better deal is 140 miles.