Latoya 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 has no initial fee but charges 60 cents for every mile driven.
Company B charges an initial fee of $65 and an additional 40 cents for every mile driven.
For what mileages will Company A charge more than Company B?
Use m for the number of miles driven, and solve your inequality for m .
Let's set up the inequality to compare the costs of the two companies:
For Company A: Cost = 0.60m
For Company B: Cost = 0.40m + 65
To find the mileages where Company A charges more than Company B, we need to find the values of m for which the cost of Company A exceeds the cost of Company B.
So, we need to solve the inequality 0.60m > 0.40m + 65.
Subtract 0.40m from both sides: 0.60m - 0.40m > 0.40m + 65 - 0.40m
0.20m > 65
Divide both sides by 0.20: (0.20m)/0.20 > 65/0.20
m > 325
Therefore, for mileages greater than 325, Company A will charge more than Company B.
To determine the mileage for which Company A charges more than Company B, we will set up an inequality based on the given information.
Let's start by defining the costs for each company:
Company A charges 60 cents for every mile driven.
Cost_A = 0.60m, where m represents the number of miles driven.
Company B charges an initial fee of $65 and an additional 40 cents for every mile driven.
Cost_B = 65 + 0.40m
To determine the mileage where Company A charges more than Company B, we need to find when Cost_A is greater than Cost_B:
Cost_A > Cost_B
0.60m > 65 + 0.40m
Now, let's solve for m:
0.60m - 0.40m > 65
0.20m > 65
Dividing both sides of the inequality by 0.20:
m > 65 / 0.20
m > 325
Therefore, for mileages greater than 325 miles, Company A will charge more than Company B.
To determine the mileages for which Company A charges more than Company B, we need to set up an inequality by comparing their costs. We'll compare the costs when renting for one day and assume that latoya is only concerned with the mileage charges.
For Company A, the cost (C_A) can be calculated using the formula: C_A = 0.6m, where m represents the number of miles driven.
For Company B, the cost (C_B) is calculated as: C_B = 0.4m + 65.
Now, we want to find the mileages (m) for which Company A charges more than Company B. In other words, we want to find the values of m that satisfy the inequality C_A > C_B.
Substituting the cost formulas into the inequality, we have:
0.6m > 0.4m + 65.
To isolate the variable, we can subtract 0.4m from both sides:
0.2m > 65.
Next, divide both sides of the inequality by 0.2:
m > 325.
Therefore, for mileages greater than 325, Company A will charge more than Company B.