Question

a truck can be rented from company a for $80 a day plus $0.20 per mile. company b charges $20 a day plus $0.70 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 bs?
for company a to have a better deal, the truck must be driven more than \\(\square\\) miles per day.

Explanation:

Step1: Define cost functions

Let $m$ = miles driven.
Cost of A: $C_A = 80 + 0.20m$
Cost of B: $C_B = 20 + 0.70m$

Step2: Set up inequality for better deal

We want $C_A < C_B$:
$80 + 0.20m < 20 + 0.70m$

Step3: Isolate $m$ terms

Subtract $0.20m$ from both sides:
$80 < 20 + 0.50m$

Step4: Isolate constant terms

Subtract 20 from both sides:
$60 < 0.50m$

Step5: Solve for $m$

Divide both sides by 0.50:
$m > \frac{60}{0.50} = 120$

Answer:

For Company A to have a better deal, the truck must be driven more than 120 miles per day.