Question

Lashonda 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 $75 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.

Answer 1

Lashonda is going to rent a truck. For mileages greater than 375 miles, company A charges more.

Solution:

Given, Lashonda 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 $75 and an additional 40 cents for every mile driven.  

We have to find for what mileages will Company A charge more than Company B?  

Let us use "m" for the number of miles driven,  

Then, charges by company A = 60cents x m = 60m

And charges by company B = $75 + 40cents x m

= 75 x 100 cents + 40m = 7500 + 40m.

Now, according to given condition,

$60 m>7500+40 m \rightarrow 60 m-40 m>7500 \\\\\rightarrow 20 m>7500 \rightarrow m>\frac{7500}{20} \\\\\rightarrow m>375$

Hence, for mileages greater than 375 miles, company A charges more