Question

Patty buys a new car and gets it appraised every few years. After owning the car for 3 years, its value is $15,000. After owning the car for 5 years, its value is $9,000. What is the constant of proportionality in this inverse variation?

Answer 1

Answer: 45000

Explanation:

From the question, we are informed that Patty buys a new car and gets it appraised every few years and that after owning the car for 3 years, its value is $15,000 and further told that after owning the car for 5 years, its value is $9,000.

Let the number of years be x

Let the value of the car be y.

From the first part of the question, we are told that after owning the car for 3 years, its value is $15,000.

Since an inverse variation will be:

x = k/y

3 = k/15000

k = 15000 × 3

k = 45000

Let's confirm the value of k for the second part of the question. After owning the car for 5 years, its value is $9,000. Here, x=5 and y = 9000

x = k/y

x = 45000/9000

x = 5

It's correct.

Therefore, the constant of proportionality is 45000