Blake is deciding between two parking garages. Garage A charges an initial fee of $10 to park plus $3 per hour. Garage B charges an initial fee of $3 to park plus $4 per hour. Let AA represent the amount Garage A would charge if Blake parks for tt hours, and let BB represent the amount Garage B would charge if Blake parks for tt hours. Write an equation for each situation, in terms of t,t, and determine which garage would be cheaper if Blake needs to park for 12 hours.

Blake can park his car in either Garage A or B. Each Garage has its own charging model (relation) for the amount of time (t) taken for the car to be parked

A general fee charging model is an explicit linear relation between the total amount charged (AA or BB) and the time (t) for which the car is parked. It consists of two parts i.e initial fee and rate charge.

To mathematically express the explicit relation we can write:

[tex]Charged Fee = Initial cost + Rate . t[/tex]

We will use the above model to express the charging fee for each garage as follows:

[tex]Garage A :\\Initial fee = 10 \\Rate = 3 \\Charged fee = 10+3. t[/tex]

[tex]Garage B :\\Initial Fee = 3\\charged fee = 4 \\Charged fee = 3+4 .t[/tex]

Once we have mathematically expressed the charging fee model of both garages we can go ahead and evaluate the fee charged if Blake wants to park his car for t=12 hours.

We will use each mathematical model and evaluate the fee for t=12 :

[tex]Garage A:\\Charged Fee = 10+ 3.(12) \\Charged Fee= 46[/tex]

[tex]Garage B:\\Charged Fee = 3+4.(12)\\Charged Fee = 51[/tex]

Therefore, the charging fee for t =12 hours is cheaper for garage B. Hence, Blake should park his car in garage B!

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