A town has a population of 18,000. If the number of males increases by 20% and the number of females increases by 15%, and the total population becomes 21,000, what is the difference between the current number of males and females?

Let the current number of males be \( x \) and the current number of females be \( y \). From the given information, the total population of the town is:

\[
x + y = 18,000 \quad \text{(equation 1)}
\]

After the increases, the number of males becomes \( 1.2x \) (a 20% increase), and the number of females becomes \( 1.15y \) (a 15% increase). The total population after the increases is 21,000, so we have:

\[
1.2x + 1.15y = 21,000 \quad \text{(equation 2)}
\]

Now, we have a system of two equations:

1. \( x + y = 18,000 \)
2. \( 1.2x + 1.15y = 21,000 \)

### Solving the system:

From equation 1, we can express \( y \) as:

\[
y = 18,000 - x
\]

Substitute this into equation 2:

\[
1.2x + 1.15(18,000 - x) = 21,000
\]

Simplify:

\[
1.2x + 1.15(18,000) - 1.15x = 21,000
\]
\[
1.2x + 20,700 - 1.15x = 21,000
\]
\[
(1.2x - 1.15x) = 21,000 - 20,700
\]
\[
0.05x = 300
\]
\[
x = \frac{300}{0.05} = 6,000
\]

So, the number of males is \( x = 6,000 \).

Now, substitute this back into equation 1 to find \( y \):

\[
6,000 + y = 18,000
\]
\[
y = 18,000 - 6,000 = 12,000
\]

### Conclusion:

The current number of males is 6,000, and the current number of females is 12,000. The difference between the number of males and females is:

\[
\boxed{6,000}
\]

Would you like further details or have any questions? 

Here are 5 questions related to this problem:

1. What would the total population be if only the males increased by 20%?
2. How would the population change if both males and females increased by 10%?
3. What if the population increase was limited to only males increasing by 25%?
4. Can you determine the percentage of the population that are females initially?
5. How would you represent this scenario graphically?

**Tip:** When solving word problems, always start by translating the conditions into algebraic equations.

Learn how to solve a population growth problem where the male population increases by 20% and the female population by 15%, resulting in a total population increase from 18,000 to 21,000. This solution uses algebraic equations and percentage increases to find the difference between the number of males and females. Suitable for students in Grades 8-10.

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