Question

Assume that the value of an automobile is inversely proportional to its age. If it is worth $3,000 when it is two years old, what is its value when it is six-years-old?

Answer 1

The car will be worth $1000 when it is 6 years old.

Explanation:

If we call the vehicle's original price when it was bought '`P`', then its price '`p`' after a time '`t`' will be given by:

`p=P/t`

This is a relationship where price is inversely proportional to age.

We don't know `P`, but we can work it out by rearranging the equation and using the data we have:

`P=pt=3000*2=6000`

So the car was originally $6000, and after 2 years is worth $3000.

After 6 years its price will be:

`p=P/t=6000/6=1000`

The car will be worth $1000 when it is 6 years old.