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 charged $114 and allows unlimited mileages
Company B has an initial fee of $65 and charges an additional $0.70 for every mile driven
For what mileages will company A charged less than company B
Use m for the number of miles driven, and solve your inequality for m
For Company A, the cost is $114 and there are no additional charges for mileage.
For Company B, the cost consists of an initial fee of $65 and an additional charge of $0.70 for every mile driven.
To find the mileage at which Company A charges less than Company B, we need to set up an inequality and solve for m (the number of miles driven).
The inequality is: 114 < 65 + 0.70m
Subtracting 65 from both sides of the inequality, we get:
49 < 0.70m
To solve for m, divide both sides of the inequality by 0.70:
m > 70
Therefore, Company A charges less than Company B when the number of miles driven is greater than 70.
To determine the mileages at which Company A charges less than Company B, we need to set up an inequality.
Let's calculate the cost function for each company:
- For Company A, the cost is a fixed amount of $114 regardless of the mileage: A(m) = 114
- For Company B, the cost consists of an initial fee of $65 plus an additional charge of $0.70 for every mile driven: B(m) = 65 + 0.70m
Now, we can set the inequality where the cost of Company A is less than the cost of Company B:
A(m) < B(m)
Substituting the cost functions:
114 < 65 + 0.70m
Next, we can simplify the inequality:
49 < 0.70m
To isolate m, divide both sides of the inequality by 0.70:
49/0.70 < m
70 < m
So, for mileages greater than 70, Company A will charge less than Company B.
To determine the mileage at which Company A charges less than Company B, we need to set up an inequality using the given information.
Let's assume that m represents the number of miles driven. The equation for Company A's cost can be expressed as a constant fee of $114, regardless of the mileage. This can be written as:
Cost of Company A: $114
On the other hand, Company B charges an initial fee of $65 and an additional $0.70 for every mile driven. Therefore, the equation for Company B's cost can be written as:
Cost of Company B: $65 + ($0.70 * m)
To find the mileage at which Company A is less expensive than Company B, we need to set up an inequality and solve for m.
Cost of Company A < Cost of Company B
$114 < $65 + ($0.70 * m)
Simplifying:
$114 < $65 + $0.70m
Subtracting $65 from both sides:
$49 < $0.70m
Dividing both sides by $0.70:
70 < m
Therefore, for any mileage value greater than 70, Company A will charge less than Company B.