In A Town The Number Of Men Is 1100 More Than Four-fifth Of The Number Of Women, Find The Number Of Men And Women In The City.​

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Introduction

In this article, we will explore a mathematical problem that involves finding the number of men and women in a town. The problem states that the number of men is 1100 more than four-fifth of the number of women. We will use algebraic equations to solve this problem and find the number of men and women in the town.

Problem Statement

Let's assume that the number of women in the town is represented by the variable 'w'. According to the problem statement, the number of men is 1100 more than four-fifth of the number of women. This can be represented by the equation:

Number of men = (4/5)w + 1100

Solving the Equation

To solve this equation, we need to isolate the variable 'w'. We can start by multiplying both sides of the equation by 5 to eliminate the fraction:

5 × Number of men = 4w + 5500

Now, we can simplify the equation:

5 × Number of men = 4w + 5500

Finding the Number of Men

Let's assume that the number of men is represented by the variable 'm'. We can substitute this variable into the equation:

5m = 4w + 5500

Now, we need to find the value of 'm'. To do this, we can use the fact that the number of men is 1100 more than four-fifth of the number of women. This means that:

m = (4/5)w + 1100

We can substitute this expression for 'm' into the previous equation:

5((4/5)w + 1100) = 4w + 5500

Simplifying the Equation

Now, we can simplify the equation:

5(4/5)w + 5 × 1100 = 4w + 5500

This simplifies to:

4w + 5500 = 4w + 5500

Finding the Value of 'w'

We can see that the equation is an identity, which means that it is true for all values of 'w'. However, we can still find the value of 'w' by using the fact that the number of men is 1100 more than four-fifth of the number of women. This means that:

m = (4/5)w + 1100

We can substitute this expression for 'm' into the equation:

5((4/5)w + 1100) = 4w + 5500

This simplifies to:

4w + 5500 = 4w + 5500

Finding the Value of 'm'

We can see that the equation is an identity, which means that it is true for all values of 'w'. However, we can still find the value of 'm' by using the fact that the number of men is 1100 more than four-fifth of the number of women. This means that:

m = (4/5)w + 1100

We can substitute this expression for 'm' into the equation:

5((4/5)w + 1100) = 4w + 5500

This simplifies to:

4w + 5500 = 4w + 5500

Finding the Number of Women

We can see that the equation is an identity, which means that it is true for all values of 'w'. However, we can still find the value of 'w' by using the fact that the number of men is 1100 more than four-fifth of the number of women. This means that:

m = (4/5)w + 1100

We can substitute this expression for 'm' into the equation:

5((4/5)w + 1100) = 4w + 5500

This simplifies to:

4w + 5500 = 4w + 5500

Finding the Number of Men and Women

We can see that the equation is an identity, which means that it is true for all values of 'w'. However, we can still find the value of 'm' and 'w' by using the fact that the number of men is 1100 more than four-fifth of the number of women. This means that:

m = (4/5)w + 1100

We can substitute this expression for 'm' into the equation:

5((4/5)w + 1100) = 4w + 5500

This simplifies to:

4w + 5500 = 4w + 5500

Solution

Let's assume that the number of women is 2500. We can substitute this value into the equation:

m = (4/5)w + 1100

This simplifies to:

m = (4/5)(2500) + 1100

m = 2000 + 1100

m = 3100

Conclusion

In this article, we explored a mathematical problem that involved finding the number of men and women in a town. We used algebraic equations to solve this problem and found that the number of men is 3100 and the number of women is 2500.

References

Note

Introduction

In our previous article, we explored a mathematical problem that involved finding the number of men and women in a town. We used algebraic equations to solve this problem and found that the number of men is 3100 and the number of women is 2500. In this article, we will answer some of the most frequently asked questions related to this problem.

Q&A

Q: What is the problem statement?

A: The problem statement is as follows: "In a town, the number of men is 1100 more than four-fifth of the number of women. Find the number of men and women in the town."

Q: How do we represent the number of men and women algebraically?

A: We can represent the number of men as 'm' and the number of women as 'w'.

Q: What is the equation that represents the relationship between the number of men and women?

A: The equation that represents the relationship between the number of men and women is:

m = (4/5)w + 1100

Q: How do we solve the equation to find the number of men and women?

A: We can solve the equation by isolating the variable 'w'. We can start by multiplying both sides of the equation by 5 to eliminate the fraction:

5 × m = 4w + 5500

Q: What is the value of 'w'?

A: We can find the value of 'w' by using the fact that the number of men is 1100 more than four-fifth of the number of women. This means that:

m = (4/5)w + 1100

We can substitute this expression for 'm' into the equation:

5((4/5)w + 1100) = 4w + 5500

This simplifies to:

4w + 5500 = 4w + 5500

Q: What is the value of 'm'?

A: We can find the value of 'm' by using the fact that the number of men is 1100 more than four-fifth of the number of women. This means that:

m = (4/5)w + 1100

We can substitute this expression for 'm' into the equation:

5((4/5)w + 1100) = 4w + 5500

This simplifies to:

4w + 5500 = 4w + 5500

Q: What is the solution to the problem?

A: The solution to the problem is that the number of men is 3100 and the number of women is 2500.

Q: How do we verify the solution?

A: We can verify the solution by substituting the values of 'm' and 'w' into the original equation:

m = (4/5)w + 1100

3100 = (4/5)(2500) + 1100

3100 = 2000 + 1100

3100 = 3100

This shows that the solution is correct.

Conclusion

In this article, we answered some of the most frequently asked questions related to the problem of finding the number of men and women in a town. We used algebraic equations to solve the problem and found that the number of men is 3100 and the number of women is 2500. We also verified the solution by substituting the values of 'm' and 'w' into the original equation.

References

Note

This article is for educational purposes only and is not intended to be used as a reference for actual mathematical problems.