Question 229439
Mack's Parking Garage charges $4.00 for the first hour and $2.50 for each additonal hour. For how long has a car been parked when the charge exceeds $16.50?


Let the total amount of hours the car has been parked at the garage be H


Then the amount of hours it has been parked at the $2.50 per hour rate is H - 1, since the 1st hour costs $4


For the total cost to exceed $16.50, we will then have:


4 + 2.5(H - 1) > 16.5


4 + 2.5H - 2.5 > 16.5


2.5H + 1.5 > 16.5


2.5H > 15


H > {{{15/2.5 = 6}}}


Therefore, for the cost to exceed $16.50, the car has to be parked a total of more than H. or more than {{{highlight_green(6)}}} hours, of which 1 hour is at the $4.00, 1st-hour rate, and more than 5 hours is at the $2.50 per hour rate.


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Check
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Since the total amount of hours is > 6, then let the total amount of hours of parking be 6.01


1 hour at $4.00  + 5.01 hours at $2.50 > $16.50 gives us:


$4.00 + 12.525 > 16.50


$4.00 + 12.53 > 16.50


$16.53 > $16.50 (TRUE)