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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.

Respuesta :

Answer:

Step-by-step explanation:

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

[tex]priceA = K\\priceB = L + Ax[/tex]

Where

[tex]K,~L~and~A~are~fixed~constants.\\x~is~the~amount~of~driven~mileage.[/tex]

Considering

[tex]K>L[/tex]

Then

[tex]priceA > priceB\\K > L + Ax\\K - L > Ax\\\frac{K - L}{A} > x[/tex]

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  [tex]\frac{K - L}{A}[/tex]. 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]

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