Question

a map of a city shaped like a square is given below on a grid. in 2003, the city’s population was 171,500 people. what was the population density in 2003? be sure to include the correct unit in your answer. population density: blank people / km² (with a grid showing a square city and unit options)

Explanation:

Step1: Find the side length of the square city

From the graph, the side length of the square (distance between two points on the grid) is \( 30 - 0 = 30 \) km (or we can check the vertical or horizontal distance, both are 30 km as it's a square).

Step2: Calculate the area of the square city

The area \( A \) of a square is given by \( A = s^2 \), where \( s \) is the side length. So \( A = 30^2 = 900 \) \( \text{km}^2 \).

Step3: Calculate the population density

Population density \( d \) is given by the formula \( d=\frac{\text{Population}}{\text{Area}} \). The population is 171500 people and the area is 900 \( \text{km}^2 \). So \( d = \frac{171500}{900}\approx190.56 \) (we can simplify the division: \( \frac{171500}{900}=\frac{1715}{9}\approx190.56 \)). But let's do the division properly: \( 171500\div900 = \frac{1715}{9}\approx190.56 \), but wait, maybe I made a mistake in side length. Wait, looking at the graph, the x - axis: from x = 0 to x = 30? Wait, no, the square has vertices at (0,0), (30,0), (30,30), (0,30)? Wait, no, the coordinates: let's check the y - axis and x - axis. Wait, the vertical side: from y = 0 to y = 30? Wait, no, the points: first point (0,0), second (30,0), third (30,30), fourth (0,30)? Wait, no, the x - axis (vertical) has marks from 0 to 70, and y - axis (horizontal) from 0 to 70. Wait, the square has vertices at (0,0), (30,0), (30,30), (0,30)? Wait, no, the vertical distance between (0,0) and (0,30) is 30 km, and horizontal distance between (0,0) and (30,0) is 30 km. So side length is 30 km. Area is \( 30\times30 = 900 \) \( \text{km}^2 \). Then population density is \( \frac{171500}{900}=\frac{1715}{9}\approx190.56 \), but maybe the side length is 35? Wait, no, the y - axis: the top point is at y = 30? Wait, no, the coordinates: let's see the y - axis (horizontal) has marks 0,10,20,30,40,... and x - axis (vertical) 0,10,20,30,40,... The square has four points: (0,0), (30,0), (30,30), (0,30). So side length is 30 km. So area is 900. Then \( 171500\div900 = 190.555...\approx191 \)? Wait, maybe I miscalculated the side length. Wait, another way: the horizontal distance between (0,0) and (30,0) is 30 units, and vertical distance between (0,0) and (0,30) is 30 units, so it's a square with side 30 km. So area is 900. Then \( 171500\div900=\frac{1715}{9}\approx190.56 \), which is approximately 191 people per \( \text{km}^2 \). But let's check the division again: 900×190 = 171000, 171500 - 171000 = 500, 500÷900≈0.56, so total≈190.56, which we can round to 191 or keep as a fraction. But maybe the side length is 35? Wait, no, the graph shows the square with vertices at (0,0), (30,0), (30,30), (0,30). So side length 30 km. So area 900. Then population density is \( \frac{171500}{900}=\frac{1715}{9}\approx190.56 \) people per \( \text{km}^2 \). But maybe I made a mistake in the side length. Wait, the problem says "a city shaped like a square". Let's re - examine the graph. The x - axis (vertical) has labels in km, from 0 to 70, with each grid line maybe 5 km? No, the first mark after 0 is 10, then 20, 30, etc. So from 0 to 30 is 30 km. So side length is 30 km. Area is 30×30 = 900. Then population density is 171500 / 900 ≈ 190.56, which is approximately 191 people per square kilometer. But let's do the division correctly: 171500 ÷ 900. Divide numerator and denominator by 100: 1715 ÷ 9. 9×190 = 1710, so 1715 - 1710 = 5, so 190 + 5/9 ≈ 190.56. So the population density is approximately 190.56 people per \( \text{km}^2 \), or if we round to a whole number, 191 people per \( \text{km}^2 \). Wait, but maybe the side length is 35? Wait, no, the coordinates: the square has vertices at (0,0), (30,0), (30,30), (0,30). So side length 30 km. So area 900. So population density is 171500 / 900 ≈ 190.56, which is about 191 people per square kilometer.

Answer:

The population density is approximately \( \boldsymbol{190.56} \) (or \( \boldsymbol{191} \) when rounded) people per square kilometer ( \( \text{people}/\text{km}^2 \) ). If we do the exact division: \( \frac{171500}{900}=\frac{1715}{9}\approx190.56 \), so the population density is approximately \( 190.56 \) \( \text{people}/\text{km}^2 \).