Question

The value of a car is inversely proportional to its age. If a car is worth $6400 when it is 3 years old, how old will it be when it is worth $2400 ? The car will be years old.

Answer 1

So, the car will be 8 years old when it is worth $2400.

If the value of a car is inversely proportional to its age, we can express this relationship using the formula:

`\[V = (k)/(A),\]`

where:

`\(V\)` is the value of the car,

`\(A\)` is the age of the car, and

`\(k\)` is the constant of proportionality.

Given that the car is worth $6400 when it is 3 years old, we can use this information to find the value of
`\(k\)`:

`\[6400 = (k)/(3).\]`

To find
`\(k\)`, multiply both sides by 3:

`\[k = 6400 * 3 = 19200.\]`

Now that we have the constant of proportionality
`(\(k\))`, we can use it to determine the age of the car when it is worth $2400. Let
`\(V = 2400\)`:

`\[2400 = (19200)/(A).\]`

To find
`\(A\)`, divide both sides by 2400:

`\[A = (19200)/(2400) = 8.\]`