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•Marble City has a population of 52,348 and covers an area of 125 square miles.


•Pebble City has the same population density as Marble City.


•The shape of Pebble City resembles a rectangle with a width of 11.8 miles and a length of x miles.


•The population of Pebble City is 85,312.


–Which measure is closest to the value of x?


Answer Choices:

A) 11

B) 17

C) 36

D) 77

Respuesta :

Population density of Marble City: 52348 / 125 = 418.784 people per sq. miles

They have same population density

85312 / 418.784 = 203.714 sq miles in Pebble City

11.8x = 203.714
x = 17.263

I guess its B but I'm not sure

Answer:

B) 17

Step-by-step explanation:

The population density is the ration between the population and the area covered. So, the population density of Marble City

[tex]M=\frac{52348}{125}\approx418.78[/tex]

If both cities have the same population density, this can be used to find the dimension of Pebble City:

[tex]P=\frac{85312}{A}\\ 418.78=\frac{85312}{A}\\A=\frac{85312}{418.78}\approx 203.72[/tex]

Now, knowing the area of Pebble City, we can find its length

[tex]A=(length)(width)\\203.72=l(11.8)\\l=\frac{203.72}{11.8}\approx 17[/tex]

Therefore, the length of Pebble City has a length of 17 miles, approximately.