Question

Susan is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

A. Company A charges an initial fee of $49 and an additional 40 cents for every mile driven.
B. Company B charges an initial fee of $30 and an additional 60 cents for every mile driven.
C. For what mileages will Company A charge no more than Company B?
D. Write your answer as an inequality, using m for the number of miles driven.

Answer 1

Company A will charge no more than Company B when the number of miles driven is greater than or equal to 95 miles. The final inequality that represents the condition is m ≥ 95. The correct answer is option d.

Step-by-step explanation:

To determine for which mileages Company A will charge no more than Company B, we need to set up an inequality.

Let m represent the number of miles driven. The cost for Company A is $49 plus $0.40 per mile, and the cost for Company B is $30 plus $0.60 per mile.

So, the inequality to represent the situation where Company A is cheaper or equal in cost to Company B is:

49 + 0.40m ≤ 30 + 0.60m

To solve this, we will subtract 0.40m from both sides and also subtract 30 from both sides to isolate m:

49 - 30 ≤ 0.60m - 0.40m

19 ≤ 0.20m

Now, divide both sides by 0.20 to solve for m:

m ≥ 95

So, Company A will charge no more than Company B when the number of miles driven is greater than or equal to 95 miles. Therefore, the correct option in the final answer is m ≥ 95 miles.