Question

a truck can be rented from company a for $140 a day plus $0.50 per mile. company b charges $60 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 variables and cost equations

Let $m$ = number of miles driven.
Cost for Company A: $C_A = 140 + 0.50m$
Cost for Company B: $C_B = 60 + 0.70m$

Step2: Set up inequality for better deal

We want $C_A < C_B$, so:
$140 + 0.50m < 60 + 0.70m$

Step3: Isolate variable terms

Subtract $0.50m$ from both sides:
$140 < 60 + 0.20m$

Step4: Isolate constant terms

Subtract 60 from both sides:
$80 < 0.20m$

Step5: Solve for $m$

Divide both sides by 0.20:
$m > \frac{80}{0.20} = 400$

Answer:

For Company A to have a better deal, the truck must be driven more than $\boldsymbol{400}$ miles per day.