A certain city with a population of 132,000 is to be divided

[Anne1276]

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 be?

a) 10,700
b) 10,800
c) 10,900
d) 11,000 - answer
e) 11,100

What is the proper, algebraic way to handle this problem? Thanks!

[Jeff]

The important insight for this problem is to realize that the way to minimize the population in the least populous voting district is to have the maximum permitted population in each of the other districts. So you have the least populous district with population, p, and then each of the remaining 10 districts would have a population 10% greater than the least populous district or 1.1p. We know the total city population is 132,000 so:

p+10*(1.1p)=132000
12p=132,000
p=11,000

/Jeff