Question

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

Company A charges $104 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.60 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.

Answer 1

To find out for what mileages Company A will charge less than Company B, we need to set up an inequality using the given prices and the number of miles driven, m.

For Company A, the cost is a flat rate of $104 regardless of the number of miles driven. Therefore, the inequality is simply:

104 < 65 + 0.60m

We can simplify this inequality by subtracting 65 from both sides:

39 < 0.60m

To isolate m, we can divide both sides by 0.60:

65 < m

So, Company A will charge less than Company B for any mileage greater than 65 miles. If Rachel plans to drive more than 65 miles, she should choose Company A to save money. However, if she plans to drive less than 65 miles, Company B may be the cheaper option.