Question

There are two parking garages in beacon falls . Garage a charges $7.00 to park for the first 2 hours ,and each additional hour costs $3.00. Garage b charges $3.25 per hour to park. When a person parks for at least 2 hours , write equations to model the cost of parking for a total of x hours ib garage a and garage b. Determine algebraically the number of hours when the cost of parking at both garages will be the same.

Answer 1

The cost equations for parking for x hours in Garage A is CA = 7 + 3(x - 2) (for x > 2) and Garage B is CB = 3.25x. Algebraically, these costs are equal after 24 hours of parking.

Step-by-step explanation:

To determine the equations for the cost of parking for a total of x hours in Garage A and Garage B, and to find the number of hours when the cost will be the same, we use algebra.

For Garage A, the cost is $7.00 for the first 2 hours and $3.00 for each additional hour. So, for x hours, the equation for the total cost (CA) is:
CA = 7 + 3(x - 2), for x > 2.

For Garage B, the cost is $3.25 per hour regardless of the number of hours. So the equation for the total cost (CB) is:
CB = 3.25x.

To find the number of hours when the cost is the same, we set CA equal to CB:
7 + 3(x - 2) = 3.25x.
Now, we solve for x:
3x - 6 = 3.25x
—6 = 3.25x – 3x
—6 = 0.25x
x = 24.

This algebraic calculation shows that after 24 hours, the cost of parking at Garage A and Garage B is the same.