Ashley 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 $124 and allows unlimited mileage
Company b has an initial fee of $75 and charges an additional $0.70 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
costA = 124
costB = 75 + .7m, where m is the number of miles driven
costA < costB
124 < 75+.7m
.7m + 75 > 124
.7m > 49
m ≥ 49/.7
m > 70
interpret my answer
To determine 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 denote the cost for Company A as 'C_A' and the cost for Company B as 'C_B'.
For Company A, the cost is a fixed $124, regardless of the mileage. So, C_A = 124.
For Company B, the cost includes an initial fee of $75 and an additional $0.70 per mile driven. Therefore, C_B = 75 + 0.70m.
To find the mileage at which Company A charges less than Company B, we set up the inequality:
C_A < C_B
124 < 75 + 0.70m
Simplifying the inequality:
0.70m > 124 - 75
0.70m > 49
Divide both sides of the inequality by 0.70:
m > 49 / 0.70
m > 70
Therefore, Company A will charge less than Company B for mileages greater than 70 miles.
To find the range of mileages for which Company A charges less than Company B, we need to compare the costs of both companies and set up an inequality.
Let's start with Company A. We know they charge a flat fee of $124 with unlimited mileage.
For Company B, they have an initial fee of $75 and charge an additional $0.70 for every mile driven. So the cost of renting with Company B can be represented as:
Cost_B = $75 + $0.70m, where m is the number of miles driven.
To find the range of mileages where Company A charges less than Company B, we need to set up an inequality and solve for m.
Cost_A < Cost_B
Substituting the values for both companies:
$124 < $75 + $0.70m
Now, let's solve the inequality for m:
$124 - $75 < $0.70m
$49 < $0.70m
Now, divide both sides by $0.70 (the coefficient of m):
$49 / $0.70 < m
70 < m
So, for Company A to charge less than Company B, the number of miles driven, represented by m, should be greater than 70. In other words, when the mileage exceeds 70 miles, Company A will have a lower cost compared to Company B.