Austin 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 $104.00 and allows unlimited mileage.
Company B has an initial fee of $65.00 and charges an additional $.60 for every mile driven.
For what mileages will Company A charge at least as much as Company B? Use m for the number of miles driven, and solve your inequality for m.
Company A:
Cost = 104
Company B:
Cost = 65 + .6m
solve:
65 + .6m ≤ 104
To determine the mileage for which Company A charges at least as much as Company B, we need to set up an inequality.
Let's assume the mileage is represented by 'm'.
For Company A, the cost is a flat fee of $104.00, regardless of the mileage.
For Company B, the cost consists of an initial fee of $65.00 plus an additional charge of $0.60 per mile driven.
So the inequality is:
104 ≥ 65 + 0.60m
Now, we can solve the inequality for 'm':
104 - 65 ≥ 0.60m
39 ≥ 0.60m
Divide both sides of the inequality by 0.60:
39/0.60 ≥ m
65 ≥ m
Therefore, for any mileage 'm' that is less than or equal to 65, Company A will charge at least as much as Company B.
To find the mileage at which Company A charges at least as much as Company B, we need to set up an inequality by equating the total costs of both companies.
For Company A, the cost is a fixed $104.00, regardless of the mileage.
For Company B, the cost consists of two parts: the initial fee of $65.00 and the cost per mile, which is $0.60 multiplied by the number of miles driven (m).
So, the total cost for Company B is $65.00 + ($0.60 * m).
Now, we need to set up the inequality:
$104.00 ≥ $65.00 + ($0.60 * m)
To simplify the inequality, subtract $65.00 from both sides:
$39.00 ≥ $0.60 * m
Now, isolate m by dividing both sides by $0.60:
$39.00 ÷ $0.60 ≥ m
Simplifying further, we get:
65 ≥ m
Therefore, for mileages equal to or greater than 65 miles, Company A will charge at least as much as Company B.