HELP PLEASE !!!
Bill 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 an initial fee of $65 and an additional 20 cents for every mile driven.
Company B charges an initial fee of $35 and an additional 70 cents for every mile driven.
For what mileages will Company A charge less than Company B?
Write your answer as an inequality, using m for the number of miles driven.
65.00 + 0.20m < 35.00 + 0.70m
To find the mileages for which Company A charges less than Company B, we need to compare their costs for different mileages.
Let's first find the cost for Company A in terms of miles driven. Company A charges an initial fee of $65 and an additional 20 cents for every mile driven. So the cost for Company A can be expressed as:
Cost_A(m) = $65 + $0.20m
Here, m represents the number of miles driven.
Similarly, let's find the cost for Company B in terms of miles driven. Company B charges an initial fee of $35 and an additional 70 cents for every mile driven. So the cost for Company B can be expressed as:
Cost_B(m) = $35 + $0.70m
Now, to find the mileages for which Company A charges less than Company B, we need to set up an inequality comparing the costs:
Cost_A(m) < Cost_B(m)
Substituting the expressions for Cost_A(m) and Cost_B(m):
$65 + $0.20m < $35 + $0.70m
Now, let's solve this inequality for m:
$65 - $35 < $0.70m - $0.20m
$30 < $0.50m
Dividing both sides by $0.50:
$60 < m
So, the inequality that represents the mileages for which Company A charges less than Company B is:
m > 60
Therefore, if Bill drives more than 60 miles, Company A will charge less than Company B.