Understanding the City Population Data

The question provides a table showing the percentage distribution of the total population across six cities (A-F) and the percentage of adult population within each city. We are given the actual population of City A and need to find the combined adult population of City B and City C as a percentage of the total population of all six cities.

The population of City A is given as 257400.

Calculating Total Population of All Six Cities

We know that the population of City A (257400) represents 23.4% of the total population of all six cities. We can use this information to find the total population.

Let the total population of all six cities be \(P_{total}\).

We have the equation:

\[ 23.4\% \text{ of } P_{total} = 257400 \] \[ \frac{23.4}{100} \times P_{total} = 257400 \] \[ P_{total} = \frac{257400 \times 100}{23.4} \] \[ P_{total} = \frac{25740000}{23.4} \]

Calculating the value:

\[ P_{total} \approx 1100000 \]

So, the total population of all six cities is approximately 1,100,000.

Calculating Adult Population in City B and City C

First, we need to find the population of City B and City C based on their percentage distribution of the total population. Then, we calculate the number of adults in each city based on their respective adult population percentages.

Population of City B:

City B has 21.6% of the total population.

Population of City B = \(21.6\%\) of \(P_{total}\)

\[ \text{Population of City B} = \frac{21.6}{100} \times 1100000 \] \[ \text{Population of City B} = 0.216 \times 1100000 \] \[ \text{Population of City B} = 237600 \]

Adult Population in City B:

68% of the population in City B are adults.

Adult population of City B = \(68\%\) of Population of City B

\[ \text{Adult Population of City B} = \frac{68}{100} \times 237600 \] \[ \text{Adult Population of City B} = 0.68 \times 237600 \] \[ \text{Adult Population of City B} = 161568 \]

Population of City C:

City C has 8.4% of the total population.

Population of City C = \(8.4\%\) of \(P_{total}\)

\[ \text{Population of City C} = \frac{8.4}{100} \times 1100000 \] \[ \text{Population of City C} = 0.084 \times 1100000 \] \[ \text{Population of City C} = 92400 \]

Adult Population in City C:

73% of the population in City C are adults.

Adult population of City C = \(73\%\) of Population of City C

\[ \text{Adult Population of City C} = \frac{73}{100} \times 92400 \] \[ \text{Adult Population of City C} = 0.73 \times 92400 \] \[ \text{Adult Population of City C} = 67452 \]

Finding Combined Adult Population of City B and City C

To find the total number of adults in City B and City C together, we add the calculated adult populations.

Combined Adult Population (B + C) = Adult Population of City B + Adult Population of City C

\[ \text{Combined Adult Population (B + C)} = 161568 + 67452 \] \[ \text{Combined Adult Population (B + C)} = 229020 \]

Percentage of Combined Adult Population to Total Population

Now, we need to express the combined adult population of City B and C as a percentage of the total population of all six cities (\(P_{total}\)).

Percentage = \(\left( \frac{\text{Combined Adult Population (B + C)}}{P_{total}} \right) \times 100\)

\[ \text{Percentage} = \left( \frac{229020}{1100000} \right) \times 100 \] \[ \text{Percentage} = 0.2082 \times 100 \] \[ \text{Percentage} = 20.82\% \]

The question asks for the percentage approximately. Looking at the options, 20.82% is approximately 21%.

Revision Table: Key Calculations

The calculated percentage, approximately 20.82%, is closest to 21% among the given options.

Additional Information: Data Interpretation Basics

Understanding how to work with percentages and distributions in data tables is crucial for solving such problems. Here are a few key points:

• Percentage Distribution: This shows how a total quantity is divided among different categories. The sum of all percentage distributions for all categories should ideally be 100%.
• Calculating Total from a Part: If you know the value of a part and its percentage of the total, you can find the total using the formula: \( \text{Total} = \frac{\text{Part Value}}{\text{Part Percentage}} \times 100 \).
• Calculating Part from Total: If you know the total and the percentage of a part, you can find the value of the part using the formula: \( \text{Part Value} = \frac{\text{Part Percentage}}{100} \times \text{Total} \).
• Percentage Calculation: To find what percentage one value (\(A\)) is of another value (\(B\)), use the formula: \( \left( \frac{A}{B} \right) \times 100 \).

These basic calculations are fundamental when analyzing data presented in tables, especially in topics like population studies, surveys, or financial reports.