Piper is deciding between two truck rental companies. Company A charges an initial fee of $35 for the rental plus $3 per mile driven. Company B charges an initial fee of $80 for the rental plus $2 per mile driven. Let AA represent the amount Company A would charge if Piper drives xx miles, and let BB represent the amount Company B would charge if Piper drives xx miles. Write an equation for each situation, in terms of x, x, and determine the interval of miles driven, x, x, for which Company A is cheaper than Company B.

An equation for each situation, in terms of x

A = 35 + 3x

B = 80 + 2x

The interval of miles driven x, for which Company A is cheaper than Company B is 0 to 44.9 miles.

Step-by-step explanation:

Let A represent the amount Company A would charge if Piper drives x miles

Let B represent the amount Company B would charge if Piper drives x miles.

Company A charges an initial fee of $35 for the rental plus $3 per mile driven.

A= $35 + $3 × x

A = 35 + 3x

Company B charges an initial fee of $80 for the rental plus $2 per mile driven.

B = $80 + $2 × x

B = 80 + 2x

The interval of miles driven x, for which Company A is cheaper than Company B.

= A < B

35 + 3x < 80 + 2x

3x - 2x < 80 - 35

x < 45 miles

That is: any number of miles driven below 45 miles makes Company A cheaper than Company B

The interval of miles driven x, for which Company A is cheaper than Company B is 0 to 44.9 miles.