Population Growth Calculation

Let the initial number of males be represented by M and the initial number of females by F.

Initial Population Setup

• Total initial population: $M + F = 50,000$

Population Growth Details

• Males increase by 10%, so the new male population is $M + 0.10M = 1.10M$.
• Females increase by 15%, so the new female population is $F + 0.15F = 1.15F$.
• The final total population is given as 56,000.

Therefore, the equation for the final population is: $1.10M + 1.15F = 56,000$

Solving for Initial Males

We have a system of two linear equations:

1. $M + F = 50,000$
2. $1.10M + 1.15F = 56,000$

From equation (1), express $F$ in terms of $M$: $F = 50,000 - M$

Substitute this expression for $F$ into equation (2): $1.10M + 1.15(50,000 - M) = 56,000$

Distribute and simplify:

• $1.10M + 57,500 - 1.15M = 56,000$
• Combine the terms with $M$: $-0.05M + 57,500 = 56,000$

Isolate the term with $M$: $-0.05M = 56,000 - 57,500$ $-0.05M = -1,500$

Solve for $M$: $M = \frac{-1,500}{-0.05}$ $M = 30,000$

The initial number of males in the town was 30,000.