Lillian is deciding between two parking garages. Garage A charges an initial fee of $4 to park plus $3 per hour. Garage B charges an initial fee of $9 to park plus $2 per hour. Let AA represent the amount Garage A would charge if Lillian parks for tt hours, and let BB represent the amount Garage B would charge if Lillian parks for tt hours. Write an equation for each situation, in terms of t, t, and determine the hours parked, t, t, that would make the cost of each garage the same.

Using a system of linear equations, the parking cost of the garage will be the same after 5 hours.

Garage A :

Garage B :

When the charges would be the same :

Equate equations (1) and (2) :

3t + 4 = 2t + 9

Collect like terms

3t - 2t = 9 - 4

t = 5

Hence, the cost will be the same after 5 hours.

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5 hours

Step-by-step explanation:

Lillian is deciding between two parking garages.

Let the time required to park be represented by t

A = Amount

From Garage A

A = the amount Garage A would charge if Lillian parks for t hours

B = the amount Garage B would charge if Lillian parks for t hours.

Garage A

Garage A charges an initial fee of $4 to park plus $3 per hour.

A = $4 + $3 × t

A = 4 + 3t

Garage B charges an initial fee of $9 to park plus $2 per hour.

B = $9 + $2 × t

B = 9 + 2t

The hours parked, t, that would make the cost of each garage the same is calculated by equating A to B

A = B

4 + 3t = 9 + 2t

Collect like terms

3t - 2t = 9 - 4

t = 5 hours

Therefore, the hours parked, t, that would make the cost of each garage the same is 5 hours

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative