a truck can be rented from company a for $90 a day plus $0.40 per mile. company b charges $50 a day plus $0.80 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?

 To find out when the rental cost for Company A becomes a better deal than Company B, we need to set up an equation where the total costs for both companies are equal, and then find out for how many miles driven this situation occurs.

Let's denote the number of miles driven as \( m \).

For Company A, the cost of renting the truck for a day is: \( Cost_A = 90 + 0.40m \)

For Company B, the cost of renting the truck for a day is: \( Cost_B = 50 + 0.80m \)

We want to find the number of miles at which the cost for Company A is less than the cost for Company B, so we first set the costs equal to each other to find the break-even point: \( 90 + 0.40m = 50 + 0.80m \)

Now we solve for \( m \):

Subtract $50 from both sides: \( 90 - 50 = 0.80m - 0.40m \)

Simplify both sides: \( 40 = 0.40m \)

Divide both sides by $0.40: \( m = 40 / 0.40 \)

\( m = 100 \)

Therefore, you must drive 100 miles for the cost of renting from Company A to be the same as the cost of renting from Company B.

Since we want to make the rental from Company A a better deal, we need to find out at what point the cost of Company A becomes less than Company B's. This happens when more than 100 miles are driven. This means that at any mileage greater than 100, Company A's rental is a better deal than Company B’s rental.