Magan is deciding between two parking garages. Garage A charges an initial fee of $7 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 Magan parks for tt hours, and let BB represent the amount Garage B would charge if Magan parks for tt hours. Write an equation for each situation, in terms of t, commat, and determine the hours parked, t, commat, that would make the cost of each garage the same.

Answer 1

To represent the costs of parking in the two garages, we can write the equations for Garage A and Garage B in terms of \( t \), which is the number of hours parked.

For Garage A:

• Initial fee: $7
• Rate per hour: $3 Thus, the equation for Garage A (denoted as \( A \)) is: \[ A = 7 + 3t \]

For Garage B:

• Initial fee: $9
• Rate per hour: $2 Thus, the equation for Garage B (denoted as \( B \)) is: \[ B = 9 + 2t \]

To find the number of hours \( t \) when the costs for both garages are equal, we set \( A \) equal to \( B \): \[ 7 + 3t = 9 + 2t \]

Now, we can solve for \( t \):

1. Subtract \( 2t \) from both sides: \[ 7 + 3t - 2t = 9 \] \[ 7 + t = 9 \]

2. Subtract 7 from both sides: \[ t = 9 - 7 \] \[ t = 2 \]

Thus, the hours parked, \( t \), that would make the cost of each garage the same is \( t = 2 \) hours.