Population Calculation Steps

We are given a total population of 900. We are also told that the number of married couples is equal to the number of singles.

Let's define the terms:

• A married couple consists of two married persons.
• Singles are individuals who are not married.

Let:

• \(M\) be the number of married couples.
• \(S\) be the number of singles.

From the problem statement, we have the condition:

\(M = S\)

The total number of married persons in the population is twice the number of married couples, because each couple includes two individuals. Let \(MP\) be the number of married persons.

\(MP = 2 \times M\)

The total population is the sum of all individuals, who are either married persons or singles.

\(\text{Total Population} = MP + S\)

We are given the total population is 900:

\(900 = MP + S\)

Now we use the condition \(M = S\) and the relationship \(MP = 2 \times M\). From \(MP = 2 \times M\), we can express \(M\) as \(M = \frac{MP}{2}\). Since \(S = M\), we also have \(S = \frac{MP}{2}\).

Substitute this expression for \(S\) into the total population equation:

\(900 = MP + \frac{MP}{2}\)

To find the value of \(MP\), we need to solve this equation. Combine the terms on the right side by finding a common denominator:

\(900 = \frac{2 \times MP}{2} + \frac{MP}{2}\)

\(900 = \frac{2MP + MP}{2}\)

\(900 = \frac{3MP}{2}\)

Now, multiply both sides of the equation by 2 to isolate the term with \(MP\):

\(900 \times 2 = 3MP\)

\(1800 = 3MP\)

Finally, divide both sides by 3 to find the value of \(MP\):

\(MP = \frac{1800}{3}\)

\(MP = 600\)

Thus, the number of married persons is 600.

Essential Population Data Analysis

The problem provides additional details about the population, such as the number of twins (100 total, 50 single) and the total number of females (400). Let's consider if this information is necessary to find the number of married persons.

• The primary condition given is the relationship between married couples and singles, alongside the total population size.
• The calculation derived (\(\text{Total Population} = MP + S\) and \(S = MP/2\)) uses only the total population and the relationship between married status groups.

The details about twins and females provide specific demographic breakdowns within the population (e.g., how many singles are twins, the gender distribution) but do not alter the overall counts of married persons and singles that sum up to the total population according to the initial conditions. Therefore, this additional information is not required to solve for the number of married persons in this particular problem.

Based on the fundamental relationship between married persons and singles given the total population, the number of married persons is calculated to be 600.