Kala is going to rent a truck for one day. There ar or two companies she can choose from and they have the following prices company a charges $117 and allows unlimited mileage. Company B has an initial fee of $65 and charges and additional $0.80 for every mile driven. For What mileage will company a charge less than Company B? Use M for the number of miles driven, and solve for your inequality for m.
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).
Let's start by considering the cost for each company.
For Company A, the price is a fixed amount of $117, regardless of the mileage. So, the cost for Company A can be represented as:
Cost(A) = $117
For Company B, there is an initial fee of $65, and an additional charge of $0.80 for every mile driven. The cost for Company B can be represented as:
Cost(B) = $65 + $0.80 * M
Now, we want to find the point at which Company A charges less than Company B. This can be expressed as an inequality:
Cost(A) < Cost(B)
Substituting the values for Cost(A) and Cost(B), we get:
$117 < $65 + $0.80 * M
Next, we can simplify the inequality:
$117 - $65 < $0.80 * M
$52 < $0.80 * M
To isolate M, we divide both sides of the inequality by $0.80:
$52 / $0.80 < M
65 < M
Therefore, if the number of miles driven, M, is greater than 65, then Company A will charge less than Company B.
So, the inequality that represents the condition is M > 65.