Question

r Flag For Review A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

Answer 1

`P = (132000)/(12)=11000`

So then P =11000 is the minimum that the least populated district could have.

Explanation:

We have a big total of N = 132000 for the population.

And we know that we divide this population into 11 districts

And we have this info given "no district is to have a population that is more than 10 percent greater than the population of any other district"

Let's assume that P represent our minimum value for a district in the population. The range of possible values for the population of each district would be between P and 1.1 P

The interest on this case is find the minimum value for P and in order to do this we can assume that 1 district present the minimum and the other 10 the maximum value 1.1P in order to find which value of P satisfy this condition, and we have this:

`P + 10 (1.1P) = 12 P= 132000`

`P = (132000)/(12)=11000`

So then P =11000 is the minimum that the least populated district could have.