Suppose that you moved to a town in which all houses are dimensionally similar (look this up) and property taxes are calculated on a formula that considers the area of the lot (10 cents/ft^2), the size of street front ($2/ft), the volume of the house (50 cents/ft^3), and the distance to the center of town ($3000 – $1 per each 100 feet away from the center).
There is a house about 1000 feet from the center of town, in a 900 ft^2 lot, which has 30 feet of street front, and pays $5000 in taxes. How much money in taxes does a house, located 3000 feet from the center of town and having 40 feet of street front, has to pay?
t = .10a + 2f + .5v + (3000 - d/100)
assuming the area and volume of the 2nd house are the same, only
2f - d/100
changes. Since the 1st house paid 5000 in taxes, and we have new variables of
d+2000 and f+10, the new taxes are
5000 + 2(10) - 20 = 5000
same taxes due
To calculate the amount of money in taxes that the house located 3000 feet from the center of town and having 40 feet of street front has to pay, we need to break down the formula for calculating property taxes based on the given parameters.
1. Area of the lot: $0.10/ft^2
2. Size of street front: $2/ft
3. Volume of the house: $0.50/ft^3
4. Distance to the center of town: $3000 – $1 per each 100 feet away from the center
Given that the first house pays $5000 in taxes, we can use this information to determine the tax rate per unit for all the parameters.
First, let's calculate the tax paid for the area of the lot:
$5000 – tax paid = area of the lot x tax rate per unit
$5000 – tax paid = 900 ft^2 x tax rate per unit for area of the lot
Solving for the tax rate per unit for the area of the lot:
tax rate per unit for area of the lot = ($5000 – tax paid) / 900 ft^2
Similarly, we can calculate the tax rates per unit for the other parameters:
- Tax rate per unit for size of street front = ($5000 – tax paid) / 30 ft
- Tax rate per unit for volume of the house = ($5000 – tax paid) / (volume of the house in ft^3)
- Tax rate per unit for distance to the center of town = ($5000 – tax paid) / (3000 ft – distance to the center of town)
Now, we can use these tax rates per unit to calculate the amount of tax for the second house, which is located 3000 feet from the center of town and has 40 feet of street front.
Tax for the area of the lot = area of the lot x tax rate per unit for area of the lot
Tax for the size of street front = size of street front x tax rate per unit for size of street front
Tax for the volume of the house = volume of the house x tax rate per unit for volume of the house
Tax for the distance to the center of town = (3000 ft – distance to the center of town) x tax rate per unit for distance to the center of town
Finally, add up these individual tax amounts to get the total tax for the second house.