Question

Josh 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 $50 and an additional 30 cents for every mile driven.
Company B has no initial fee but charges 80 cents for every mile driven.
For what mileages will Company A charge at least as much as Company B?

Answer 1

Josh should choose Company A if he plans to drive 100 miles or less, as it would cost the same or less than Company B. For mileages above 100 miles, Company B will be the cheaper option. We solved this comparing the costs of both companies and finding the mileage at which they are equal.

Step-by-step explanation:

For what mileages will Company A charge at least as much as Company B?

To determine when Company A will charge at least as much as Company B, we can set up an inequality. Let m represent the miles driven. For Company A, the cost is $50 plus $0.30 per mile, so the cost is given by 50 + 0.30m. For Company B, the cost is $0.80 per mile, so the cost is given by 0.80m. We want to find when Company A's cost is at least as much as Company B's cost, so we set up the inequality: 50 + 0.30m ≥ 0.80m.

To solve the inequality:

Subtract 0.30m from both sides: 50 ≥ 0.50m.

Divide both sides by 0.50: m ≥ 100.

Therefore, when Josh drives more than 100 miles, Company A will charge at least as much as Company B.