London is deciding between two truck rental companies. Company A charges an initial fee of $40 for the rental plus $2.50 per mile driven. Company B charges an initial fee of $100 for the rental plus $1 per mile driven. Let A represent the amount Company A would charge if London drives x miles, and let B represent the amount Company B would charge if London drives x miles. Write an equation for each situation, in terms of x, and determine the interval of miles driven, x, for which Company A is cheaper than Company B.

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joaobezerra joaobezerra · Answer 1 · 2022-08-24T17:41:45+02:00

Using linear functions, we have that Company A is cheaper than Company B for distances of less than 40 miles.

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, we consider that:

Hence the functions are:

Company A is cheaper when:

A(x) < B(x)

40 + 2.5x < 100 + x

1.5x < 60

x < 60/1.5

x < 40.

For distances of less than 40 miles, company A is cheaper.

More can be learned about linear functions at https://brainly.com/question/24808124

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