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 fort
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

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

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

2. 8 hours

Explanation:

For park A,

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

where A is the amount paid, and t is the number of hours.

For park B,

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

where B is the amount paid, and t is the number of hours.

The hours that would make A = B can be determined as follows.

Equate 1 and 2, so that;

A = B

4 + 3t = 12 + 2t

collect like terms

3t - 2t = 12 - 4

t = 8

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