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The village of Clemson has a population density of 15 people per square mile. Neighboring Quimbly has a population density of 8 people per square mile. If the area of both villages combined is 200 square miles, which of the following could be the population of both villages combined?


A) 1500
B) 3050
C) 2800
D) 1575

Respuesta :

onyebuchinnaji

The population of both villages combined is 2,800

The given parameters;

  • population density of the Clemson = 15 people per square mile
  • population density of Quimbly = 8 people per square mile
  • area of both villages combined = 200 square mile

Let the area of village Clemson = a

Let the area of village Quimbly = b

The total area of both villages:

a + b = 200

The population of both villages combined is calculated as;

15a + 8b = T

where;

  • T is the population of both villages combined

The maximum number of the population of both villages will occur when;

a = 199 and b = 1

15(199) + 8(1) = 2993

The minimum number of the population of both villages will occur when;

a = 1 and b = 199

15(1) + 8(199) = 1607

The population of both villages combined is between 1607 and 2993;

1607 ≤ T ≤ 2,993

In the given options, the only number within this range is 2,800

Thus, the population of both villages combined is 2,800

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