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Aaliyah is deciding between two parking garages. Garage A charges an initial fee of $8 to park plus $2 per hour. Garage B charges an initial fee of $4 to park plus $3 per hour. Let AA represent the amount Garage A would charge if Aaliyah parks for tt hours, and let BB represent the amount Garage B would charge if Aaliyah parks for tt hours. Graph each function and determine the interval of hours parked, t,t, for which Garage A is cheaper than Garage B.

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raphealnwobi

The interval of hours for which Garage A is cheaper than Garage B is t > 4.

Let A represent the amount Garage A would charge if Aaliyah parks for t hours, and let B represent the amount Garage B would charge if Aaliyah parks for t hours.

Garage A charges an initial fee of $8 to park plus $2 per hour. Hence:

A = 2t + 8  

Garage B charges an initial fee of $4 to park plus $3 per hour. Hence:

A = 3t + 4

For Garage A to be cheaper than Garage B:

2t + 8 < 3t + 4

8 - 4 < 3t - 2t

4 < t

t > 4

The interval of hours for which Garage A is cheaper than Garage B is t > 4.

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