How much ore for how much iron?

Haematite is $70\ \%$ iron, and a real ore is only partly haematite. You will make the program work backwards from the iron a factory wants to the haematite and the ore it must dig, and the gangue that comes with it.

The idea. Haematite needed = iron ÷ $0.70$. Ore needed = haematite ÷ purity. Gangue = ore − haematite.

Your tasks.

1. In haematite_needed, return the haematite for a mass of iron.
2. In ore_needed, return the ore for a mass of iron, given the purity.
3. Find gangue, the waste dug up to make $1000\ \text{kg}$ of iron from an $80\ \%$ ore.