Question

kareem is going to rent a truck for one day. there are two companies he can choose from, and they have the following prices.
company a charges an initial fee of $60 and an additional 80 cents for every mile driven.
company b charges an initial fee of $55 and an additional 90 cents for every mile driven.
for what mileages will company a charge no more than company b?
write your answer as an inequality, using m for the number of miles driven.

Explanation:

Step1: Define cost functions

Let $m$ = miles driven.
Cost of Company A: $60 + 0.80m$
Cost of Company B: $55 + 0.90m$

Step2: Set up inequality

We want Company A cost ≤ Company B cost:
$$60 + 0.80m \leq 55 + 0.90m$$

Step3: Subtract 55 from both sides

$$5 + 0.80m \leq 0.90m$$

Step4: Subtract $0.80m$ from both sides

$$5 \leq 0.10m$$

Step5: Solve for $m$

$$m \geq \frac{5}{0.10}$$
$$m \geq 50$$

Answer:

$m \geq 50$