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?

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Answer 1 · 2017-07-15T22:18:23

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

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

$p = \frac{P}{t}$ $p=P/t$

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

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

$P = p t = 3000 \cdot 2 = 6000$ $P=pt=3000*2=6000$

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

After 6 years its price will be:

$p = \frac{P}{t} = \frac{6000}{6} = 1000$ $p=P/t=6000/6=1000$

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