Realtors in a Florida community have found that the average price of a four bedroom house varies inversely with the distance that the house lies away from the beach. If, on average a four bedroom house located 2 miles from the beach cost $750,000, What is the average cost of house that lies 5 miles from the beach?
pr = k(1/d)
when d = 2, pr = 750000
750000 = k(1/2)
k = 1500000
so pr = 150000(1/d)
if d = 5
pr = 150000(1/5)
= $300,000
To find the average cost of a house that is 5 miles away from the beach, we can use the inverse variation relationship. In inverse variation, the general form of the equation is y = k/x, where y and x are two related variables, and k is the constant of variation.
In this case, the average cost of a four bedroom house is the y variable, and the distance from the beach is the x variable. We are given that a house located 2 miles from the beach costs $750,000, so we can use this information to find the value of the constant k.
Substituting the given values into the inverse variation equation, we have:
750,000 = k/2
To find the value of k, we can isolate it by multiplying both sides of the equation by 2:
2 * 750,000 = k
k = 1,500,000
Now that we have the value of the constant of variation, we can find the average cost of a house that is 5 miles away from the beach by substituting the distance into the equation:
y = k/x
y = 1,500,000/5
y = 300,000
Therefore, the average cost of a house that is 5 miles away from the beach is $300,000.