The total population of a town is 50,000. The number of males and females increases by 10% and 15%, respectively, and consequently, the population of the town becomes 56,000. What was the number of males in the town?

Question

Accepted Answer

Let the number of males in the town be $$ x $$, and the number of females be $$ 50,000 - x $$.

#### Step 1: Population After Increase
- Male population after a 10% increase:  
  $$ 1.1x $$  
- Female population after a 15% increase:  
  $$ 1.15(50,000 - x) $$

The total population after the increase is given as $$ 56,000 $$. Thus:  
$$
1.1x + 1.15(50,000 - x) = 56,000
$$

#### Step 2: Simplify the Equation
Expand and simplify:  
$$
1.1x + 57,500 - 1.15x = 56,000
$$  
Combine like terms:  
$$
-0.05x + 57,500 = 56,000
$$  
$$
-0.05x = -1,500
$$  
Solve for $$ x $$:  
$$
x = \frac{-1,500}{-0.05} = 30,000
$$

#### Step 3: Verify the Solution
- Males: $$ x = 30,000 $$, after a 10% increase: $$ 1.1 	imes 30,000 = 33,000 $$.  
- Females: $$ 50,000 - x = 20,000 $$, after a 15% increase: $$ 1.15 	imes 20,000 = 23,000 $$.  
- Total population after increase: $$ 33,000 + 23,000 = 56,000 $$.

Thus, the initial number of males was **30,000**.

Answer

Answer

Answer