A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least population district could have?
A 10700 B 10800 C 10900 D 11000 E 11100
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bluementor
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this question belongs in the PS sub-forum.
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In order for a district to have minimum population, the rest of the 10 districts must have the maximum population possible.
x = minimum population
y = maximum population
And since no district can have a population 10% greater than any other population, we have:
y = 1.1x
therefore, we have 10 districts with population y and 1 district with population x:
total population = 132000
x + 10y = 132000
x + 10(1.1x) = 132000
x + 11x = 132000
12x = 132000
x = 11000
Choose D.
-BM-
______________________________
In order for a district to have minimum population, the rest of the 10 districts must have the maximum population possible.
x = minimum population
y = maximum population
And since no district can have a population 10% greater than any other population, we have:
y = 1.1x
therefore, we have 10 districts with population y and 1 district with population x:
total population = 132000
x + 10y = 132000
x + 10(1.1x) = 132000
x + 11x = 132000
12x = 132000
x = 11000
Choose D.
-BM-
