Ravi 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 $75 and allows unlimited mileage.
Company B has an initial fee of $55 and charges an additional $0.80 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.
Acost=75
Bcost=55+.8m
75>44+.8m solve for m.
70
To determine the mileage at which Company A charges less than Company B, we can set up an inequality:
Company A cost < Company B cost
The cost for Company A is a flat fee of $75, regardless of the mileage driven.
The cost for Company B is an initial fee of $55, plus $0.80 for every mile driven.
Therefore, the inequality can be written as:
75 < 55 + 0.80m
To solve for m (mileage), we can subtract 55 from both sides of the inequality:
20 < 0.80m
Then, divide both sides of the inequality by 0.80:
20/0.80 < 0.80m/0.80
25 < m
So, for any mileage greater than 25 miles, Company A will charge less than Company B.
To compare the prices between Company A and Company B, we need to set up an inequality and solve it for the number of miles driven, represented by 'm'.
Let's first look at Company A's charges: $75 for unlimited mileage. This means that regardless of how many miles Ravi drives, he will always be charged $75.
Now, let's consider Company B's charges. It has an initial fee of $55 and an additional charge of $0.80 for every mile driven. Therefore, the total cost for Company B can be calculated as: $55 (initial fee) + $0.80 (cost per mile) * m (number of miles driven).
To find the mileage at which Company A charges less than Company B, we need to set up the inequality:
Company A's cost < Company B's cost
$75 < $55 + $0.80 * m
Simplifying the equation, we get:
$75 < $55 + $0.80m
Now, we can solve this inequality for 'm' to find the range of mileages where Company A charges less than Company B:
$75 - $55 < $0.80m
$20 < $0.80m
Divide both sides by $0.80:
25 < m
Therefore, for any mileage greater than 25 miles, Company A will charge less than Company B.