Question

Kaitlin 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 a fixed fee and allows unlimited mileage. Company B has an initial fee and charges an additional fee for every mile driven. For what mileages will Company A charge less than Company B? Use for the number of miles driven, and solve your inequality form.

Answer 1

Explanation:

According to the information given in the statement, there are the following mathematical expressions:

`priceA = K\\priceB = L + Ax`

Where

`K,~L~and~A~are~fixed~constants.\\x~is~the~amount~of~driven~mileage.`

Considering

`K>L`

Then

`priceA > priceB\\K > L + Ax\\K - L > Ax\\(K - L)/(A) > x`

The last equation means that to maintain the [text]priceB[\text] lower than [text]priceA[\text], the amount of driven mileage must be less than
`(K - L)/(A)`. If [tex]x[\tex] becomes greater than the fraction, then the [text]priceA[\text] will be lower than [text]priceB[\text].

[tex]\frac{K - L}{A} < x \\ K - L < Ax \\ K < L + Ax[\tex]