Question

Isabella 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 $12 to park plus $2 per
hour. Let A represent the amount Garage A would charge if Isabella parks for t
hours, and let B represent the amount Garage B would charge if Isabella parks for t
hours. Write an equation for each situation, in terms oft, and determine the hours
parked, t, that would make the cost of each garage the same.

Answer 1

i. A = 4 + 3t .......... 1

B = 12 + 2t .......... 2

ii. The hours required would be 8 hours.

Explanation:

The charges at each of the garages can be expressed as;

i. For garage A,

A = 4 + 3t .......... 1

ii. For garage B,

B = 12 + 2t .......... 2

where A is the amount charged at garage A, B is the amount charged at garage B, and t is the number of hours.

To determine the number of hours parked that would make the cost of each garage the same.

Let:

equation 1 = equation 2

4 + 3t = 12 + 2t

collect like terms

3t - 2t = 12 - 4

t = 8

The hours that would make the cost of each garage the same is 8 hours.