Inverse Variation!?

Question

Ok I'm having my GCE O levels examination in like 5 hours, so reaaaally need help on this question.

The force of attraction between two magnets if F Newtons. This force is inversely proportional to the square of the distance, D centimetres, between the magnets.

When the magnets are a certain distance apart, the forcce is 10 Newtons. What is the force when this distance is doubled?

Answer 1

"inversely proportional to the square of the distance" means "equals a constant divided by the square of the distance".

So F = k/D² for some number k.

Ordinarily, you are told what the force is when the magnets are a particular stated distance apart, which enables you to find the constant k. This problem is a bit different. They say that for some (unspecified) distance, the force is 10 Newtons, and then they ask what the force will be if the distance is made twice that.

So, for some specific distance d, we have

10 = k/d²

Then, if the distance is doubled, the force is given by

F = k/(2d)² = k/(4d²) = (k/d²)/4 = 10/4 = 2.5 Newtons