Question

a truck can be rented from company a for $140 a day plus $0.30 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 cost functions

Let \( x \) be the number of miles driven.
Cost for Company A: \( C_A = 140 + 0.30x \)
Cost for Company B: \( C_B = 60 + 0.70x \)

Step2: Set up inequality for better deal

We want \( C_A < C_B \):
\( 140 + 0.30x < 60 + 0.70x \)

Step3: Solve the inequality

Subtract \( 0.30x \) from both sides:
\( 140 < 60 + 0.40x \)

Subtract 60 from both sides:
\( 80 < 0.40x \)

Divide both sides by \( 0.40 \):
\( x > \frac{80}{0.40} = 200 \)

Answer:

200