Charlie 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 $127 and allows unlimited mileage.
Company B has an initial fee of $55.00 and charges an additional $0.90 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 .
a=127
b=55+.9m
127=55+.9m
72=.9m
m=80
To determine the mileage at which Company A charges at least as much as Company B, we need to set up an inequality.
Let's denote the mileage as 'm' and the total cost as 'C'.
For Company A, the total cost is a fixed price of $127, regardless of the mileage: C(A) = $127.
For Company B, the total cost consists of the initial fee of $55 and an additional charge of $0.90 per mile: C(B) = $55 + $0.90m.
To find the mileages where Company A charges at least as much as Company B, we need to set up the inequality:
C(A) ≥ C(B)
Substituting the expressions for C(A) and C(B):
$127 ≥ $55 + $0.90m
Now, let's solve this inequality for 'm':
$127 - $55 ≥ $0.90m
$72 ≥ $0.90m
Divide both sides by $0.90:
$80 ≥ m
Therefore, Company A will charge at least as much as Company B for any mileage equal to or greater than $80.