Question

Bella 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 $3 to park plus $4 per hour.
Let A represent the amount Garage A would charge if Bella parks for t hours, and let
B represent the amount Garage B would charge if Bella parks for t hours. Write an
equation for each situation, in terms of t, and determine the hours parked, t, that
would make the cost of each garage the same.

Answer 1

Bella 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 $3 to park plus $4 per hour.

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

B represent the amount Garage B would charge if Bella parks for t hours. Write an

equation for each situation, in terms of t, and determine the hours parked, t, that

would make the cost of each garage the same.

A = $7 + $3

B = $3 + $4

Answer 2

Explanation:

The equation for the cost of parking in Garage A for t hours is:

A = 3t + 7

The equation for the cost of parking in Garage B for t hours is:

B = 4t + 3

To find the number of hours parked, t, that would make the cost of each garage the same, we can set the two equations equal to each other and solve for t:

3t + 7 = 4t + 3

Subtracting 3t from both sides, we get:

7 = t + 3

Subtracting 3 from both sides, we get:

4 = t

Therefore, if Bella parks for 4 hours, the cost of parking in Garage A and Garage B will be the same.

To verify, we can substitute t = 4 into the two equations:

A = 3(4) + 7 = 19

B = 4(4) + 3 = 19

So, if Bella parks for 4 hours, the cost of parking in Garage A and Garage B will be $19.