SOLUTION: 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?

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?
Found 2 solutions by checkley77, MathTherapy:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
4+2.50X>16.50
2.50X>>16.50-4
2.50X>12.50
X>12.50/2.50
X>5 HOURS.
1 HOUR @ %4.00 + 5 HOURS @ $2.50=16.50
PROOF:
LET THE HOURS @ 2.50 BE 5.1 HOURS.
4+2.50*5.1>16.50
4+12.75>16.50
16.75>16.50

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
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 >

Therefore, for the cost to exceed $16.50, the car has to be parked a total of more than H. or more than 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)
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