The populations and land areas of four cities in Texas are shown.
| | Population | Area ($km^2$) |
| :------- | :---------- | :------------ |
| City A | $2,195,914$ | 1,553 |
| City B | 48,592 | 26 |
| City C | $1,257,676$ | 999 |
| City D | 196,429 | 258 |
Which statements are true? Select three options.
A. The population density for City B can be found using the ratio $48,592: 26$.
B. The population density for City D can be found using the ratio $258: 196,429$.
C. City $A$ has the greatest population density of the four cities.
D. The population density of City B is greater than that of City C.
E. City D has the lowest population density of the four cities
Answer (1)
Calculate the population density for each city by dividing its population by its area.
Verify that the population density for City B can be found using the ratio 48 , 592 : 26 .
Confirm that City B's population density is greater than City C's.
Check that City D has the lowest population density among the four cities. The three true statements are then selected. The true statements are: The population density for City B can be found using the ratio 48 , 592 : 26 , The population density of City B is greater than that of City C, and City D has the lowest population density of the four cities.
Explanation
Understanding the Problem We are given the populations and land areas of four cities and need to determine which of the given statements about their population densities are true. Population density is calculated by dividing the population by the area.
Calculating Population Densities First, let's calculate the population densities for each city:
City A: Population Density = 1 , 553 2 , 195 , 914 ≈ 1413.98 people per k m 2 City B: Population Density = 26 48 , 592 ≈ 1868.92 people per k m 2 City C: Population Density = 999 1 , 257 , 676 ≈ 1258.93 people per k m 2 City D: Population Density = 258 196 , 429 ≈ 761.35 people per k m 2
Evaluating the Statements Now, let's evaluate the given statements:
The population density for City B can be found using the ratio 48 , 592 : 26 . This is true because population density is population divided by area, which is the same as the ratio of population to area.
The population density for City D can be found using the ratio 258 : 196 , 429 . This is false because the ratio is inverted. It should be 196 , 429 : 258 .
City A has the greatest population density of the four cities. This is false. City B has the greatest population density ( 1868.92 people per k m 2 ).
The population density of City B is greater than that of City C. This is true because 1258.93"> 1868.92 > 1258.93 .
City D has the lowest population density of the four cities. This is true because 761.35 is the lowest among the four cities.
Identifying True Statements Therefore, the three true statements are:
The population density for City B can be found using the ratio 48 , 592 : 26 .
The population density of City B is greater than that of City C.
City D has the lowest population density of the four cities.
Examples
Understanding population density is crucial in urban planning and resource management. For example, knowing the population density helps city planners allocate resources effectively, such as building schools, hospitals, and transportation infrastructure. A higher population density might require more public transportation options or more frequent garbage collection services. By analyzing population density, cities can better meet the needs of their residents and ensure a higher quality of life.
