A parking lot charges $3 to park a car for the first hour and $2 per hour after that. If you use more than one parking space, the second and each subsequent car will be charged 75% of what you pay to park just one car. If you park 3 cars for t hours, which function gives the total parking charge?
If you park n cars for t hours,
car 1: x = 3 + 2(t-1)
others: 3/4 that amount, or 3/4 (n-1)*x
So, the total amount will be
f(n,t) = (3+2(t-1))(1 + (3/4)(n-1))
= (3n+1)(2t+1)/4
So, 3 cars for t hours is
f(3,t) = 5/2 (2t+1)
So, let's check, say, f(3,4)=45/2=$22.50
1st car: 3 + 2*3 = 9
other 2 cars: each 3/4 of that amount, or 2*27/4 = $13.50
Total: $22.50
A parking lot charges a flat rate of x dollars for any amount of time up to two hours, and x
6
1
for
each hour or fraction of an hour after the first two hours. How much does it cost to park for 5 hours
and 15 minutes?
To calculate the total parking charge for parking 3 cars for t hours, we need to consider the charges for each car.
The first car costs $3 for the first hour, and $2 per hour after that.
For t-1 hours after the first hour, the cost will be (t-1) * $2.
The second car will be charged 75% of what is paid for the first car. So the cost for the second car for t hours will be (0.75 * $3) + (0.75 * (t-1) * $2).
The third car will also be charged 75% of what is paid for the first car. So the cost for the third car for t hours will be (0.75 * $3) + (0.75 * (t-1) * $2).
To find the total parking charge, we add up the charges for each car:
Total charge = (cost of first car) + (cost of second car) + (cost of third car)
Total charge = ($3) + [(0.75 * $3) + (0.75 * (t-1) * $2)] + [(0.75 * $3) + (0.75 * (t-1) * $2)]
Simplifying the equation:
Total charge = $3 + ($2.25 + 0.75t - 0.75) + ($2.25 + 0.75t - 0.75)
Total charge = $3 + $2.25 + $2.25 + 0.75t + 0.75t - 0.75 - 0.75
Total charge = $8.25 + 1.5t
The function that gives the total parking charge is: Total charge = $8.25 + 1.5t.
To find the total parking charge for parking 3 cars for t hours, we need to consider the different charges for each car and the total hours parked.
Let's break down the total parking charge step by step:
1. For the first car:
- The first hour costs $3.
- For each subsequent hour, it costs $2.
So, for t hours, the charge for the first car can be expressed as:
Charge for the first car = $3 + ($2 * (t - 1)).
2. For the second and subsequent cars:
- The charge for the second car is 75% of what you pay to park just the first car.
- The charge for any subsequent car is also 75% of the charge for the first car.
So, the charge for the second and subsequent cars can be expressed as:
Charge for the second and subsequent cars = 75% * (Charge for the first car).
3. Total parking charge:
To find the total parking charge for all 3 cars, we need to add the charges for each car. Keep in mind that the second and subsequent cars have a reduced charge. Therefore:
Total parking charge = (Charge for the first car) + (Charge for the second and subsequent cars) + (Charge for the second and subsequent cars).
In mathematical terms, the function giving the total parking charge for 3 cars parked for t hours can be represented as:
Total Parking Charge = ($3 + ($2 * (t - 1))) + 2*(75% * ($3 + ($2 * (t - 1)))).
or, simplifying further:
Total Parking Charge = ($3 + ($2 * (t - 1))) + 1.5 * ($3 + ($2 * (t - 1))).
This function accounts for the charges for the first car as well as the reduced charges for the second and subsequent cars.