This is math in geography!

Algebra Level 3

A group of geographers analysing the 2013 data of two cities found that the city A had a population of 250,000 habitants, and it have an area of $1250 \text{ km}^{2}$ .

The data of city B was incomplete and the only informations are that the ratio between city A population and city B population was 2:3 and the population density of city B was 100 habitants per kilometre square less than city A .

Then, the area of city B is:

Definitions: The Population Density of a city is the average number of habitants living in each kilometer square of this city.

3 times larger than city A 1.5 times smaller than city A The same area of city A 3 times smaller than city A 1.5 times larger than city A

1 solution

Hung Woei Neoh
May 7, 2016

Now, let area be $a$ , population be $p$ and population density be $d$ .

$p_A = 250000, a_A = 1250\\ \implies d_A = \dfrac{250000}{1250} = 200$

Now, we know that

$p_A: p_B = 2:3\\ \dfrac{p_A}{p_B} = \dfrac{2}{3}\\ p_B = \dfrac{3}{2}p_A = \dfrac{3}{2} \times 250000 = 375000$

We also know that

$d_B = d_A - 100 = 200 - 100 = 100$

Now, we can find $a_B$ :

$100 = \dfrac{375000}{a_B}\\ a_B = \dfrac{375000}{100} = 3750$

$3750 = 1250 \times 3 \implies a_B = 3a_A$

Therefore, area of city B is $\boxed{\text{3 times larger than city A}}$

This is math in geography!

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