Understanding the Population Distribution Data

The question provides a table showing the percentage distribution of the total population across six cities (A, B, C, D, E, F) and the percentage of the adult population within each of these cities. We are also given the total population of City A. Our goal is to find the adult population of City C.

First, let's look at the data provided in the table:

We are given that the population of City A is 257400. According to the table, City A represents 23.4% of the total population of all six cities combined.

Step-by-Step Calculation of Adult Population in City C

Here are the steps to calculate the adult population in City C:

1. Calculate the total population of all six cities.
2. Calculate the total population of City C.
3. Calculate the adult population of City C.

Step 1: Calculate the Total Population

The population of City A (257400) is 23.4% of the total population. Let the total population be \(T\). We can write this relationship as:

\(23.4\%\) of \(T = 257400\)

Converting the percentage to a decimal (\(23.4\% = 0.234\)):

\(0.234 \times T = 257400\)

Now, solve for \(T\):

\(T = \frac{257400}{0.234}\)

\(T = 1100000\)

So, the total population of all six cities is 1100000.

Step 2: Calculate the Population of City C

According to the table, City C represents 8.4% of the total population. We use the total population \(T = 1100000\) calculated in Step 1.

Population of City C = \(8.4\%\) of \(1100000\)

Converting the percentage to a decimal (\(8.4\% = 0.084\)):

Population of City C = \(0.084 \times 1100000\)

Population of City C = \(92400\)

The total population of City C is 92400.

Step 3: Calculate the Adult Population of City C

The table shows that 73% of the population in City C is adult. We use the population of City C (92400) calculated in Step 2.

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

Adult Population of City C = \(73\%\) of \(92400\)

Converting the percentage to a decimal (\(73\% = 0.73\)):

Adult Population of City C = \(0.73 \times 92400\)

Adult Population of City C = \(67452\)

Therefore, the adult population of City C is 67452.

Conclusion

By first finding the total population using the data for City A, and then using the percentage distribution and adult percentage for City C, we calculated the adult population in City C.

The calculated adult population of City C is 67452.

Revision Table: Key Data Points

Additional Information: Understanding Percentage Distribution

Percentage distribution tables, like the one in this question, are common in data interpretation problems. They show how a total quantity (in this case, total population) is divided among different categories (the six cities). To solve problems involving such tables, it's often necessary to first calculate the total quantity if a specific value for one category is given along with its percentage.

• The sum of the percentage distributions for all categories should ideally add up to 100% (or very close to it, allowing for minor rounding). In this table: \(23.4 + 21.6 + 8.4 + 18.9 + 17.5 + 10.2 = 100\%\).
• The percentage of the adult population is specific to each city; it's not a percentage of the total population of all cities, but a percentage of the population within that particular city.
• To find the actual number for a percentage, convert the percentage to a decimal by dividing by 100, then multiply by the total value. For example, 73% of 92400 is \(0.73 \times 92400\).

Solving these problems requires careful reading of the table and understanding which percentage relates to which total (total population of all cities vs. total population of a single city).