# How to determine (lost) surface (km²) of a country when both population and population density have changed? [closed]

I am not sure if the question suits in this stack board, but I give it a try.

Let's assume there is a country with a population of 327 million people and a surface of 9.6 million km², resulting in 34 inhabitants per km².

Now, let's say we have a fictive war scenario, in which the country loses and has to give up land to the victors. The population sunk to 100 million people and 10 inhabitants per km² (still assuming that surface was given to victors, thus the country now has a smaller surface!!). How would I calculate the new surface with these two (now changed) variables or would I need more data?

My question now is:

Is it still possible to determine the new surface of the country when both population and population density changed?

I tried many ways to accomplish that, but I really have no idea how to approach it. Maybe it's possible with a system of linear equations? I have no idea.

## closed as off-topic by Jan Doggen, Deditos, gansub, arkaia, FredFeb 11 at 16:12

• This question does not appear to be about earth science, within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

• was americas land area smaller before the europeans discovered it,it is related to the logic of your question. – trond hansen Feb 8 at 10:56
• Sorry but this has noting to with Earth Science. It's an elemental math question. If X/Y=Z, and I know X and Z, can I calculate Y? Of course you can. – Jan Doggen Feb 10 at 14:03
• I'm voting to close this question as off-topic because it just a mathematical question that has nothing to do with Earth Science – Jan Doggen Feb 11 at 8:51

$$\text{Poulation density} = \frac{\text{Population}}{\text{Surface}}$$

Re-arranging

$$\text{Surface} = \frac{\text{Population}}{\text{Poulation density}}$$

$$\text{Surface} = \frac{100,000,000\, \text{inhabitants}}{10\, \text{inhabitants}\, \text{km}^{-2}}=10,000,000\, \text{km}^2$$