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?

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

Solution

To determine how many miles must be driven in a day for Company A to be a better deal than Company B, follow these steps: Let \( x \) represent the number of miles driven in a day. For Company A: \[ \text{Cost}_A = 180 + 0.40x \] For Company B: \[ \text{Cost}_B = 30 + 0.90x \] Set up the inequality where Company A’s cost is less than Company B’s cost: \[ 180 + 0.40x < 30 + 0.90x \] Subtract \( 0.40x \) from both sides: \[ 180 < 30 + 0.50x \] Subtract 30 from both sides: \[ 150 < 0.50x \] Divide both sides by 0.50: \[ 300 < x \] Therefore, the truck must be driven more than \( 300 \) miles per day for Company A to be the better deal.