Maria 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 an initial fee of $55 and an additional 90 cents for every mile driven. company b charges an initial fee of $90 and an additional 40 cents for every mile driven. for what mileages will company a charge less than company b?

for mileage less than 70 miles Company A will charge less than Company B

Explanation:

Data provided in the question:

initial fee of Company A = $55

additional cents for every mile driven for company A = 90 = $0.90

initial fee of Company B = $90

additional cents for every mile driven for company B = 40 = $0.40

let the minimum miles for which Company A charge less than Company B be 'x' miles

Now,

The Total rent function for company A

= Initial fees + charges for total miles driven

= $55 + $0.90x  (1)

and,

The Total rent function for company B

= Initial fees + charges for total miles driven

= $90 + $0.40x     (2)

for the condition Company A charge less than Company B

equation 1 < equation 2

or

$55 + $0.90x < $90 + $0.40x

or

$0.90x - $0.40x < $90 - $55

or

$0.50x < $35

or

x < 70 miles

hence,

for mileage less than 70 miles Company A will charge less than Company B

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