Understanding the Revenue Equation

Oct 13, 2025 by miodeya.com 27 views

Introduction

In the world of business, understanding the revenue generated from different products is crucial for making informed decisions. A company that sells two types of office chairs has reported a total revenue of $\$3,200$ last month. The revenue equation $55m + 85n = 3,200$ represents this situation, where $m$ is the number of basic chairs sold and $n$ is the number of deluxe chairs sold. In this article, we will delve into the world of linear equations and solve for the number of basic and deluxe chairs sold to meet the total revenue of $\$3,200$ .

Understanding the Revenue Equation

The revenue equation $55m + 85n = 3,200$ can be broken down into two parts: the revenue generated from basic chairs and the revenue generated from deluxe chairs. The coefficient of $m$ represents the revenue generated from each basic chair, which is $\$55$ . Similarly, the coefficient of $n$ represents the revenue generated from each deluxe chair, which is $\$85$ . The constant term $3,200$ represents the total revenue generated from both types of chairs.

Solving the Equation

To solve the equation $55m + 85n = 3,200$ , we need to find the values of $m$ and $n$ that satisfy the equation. One way to do this is by using the method of substitution or elimination. In this case, we will use the method of substitution.

Method of Substitution

We can start by isolating one of the variables, say $m$ . We can do this by subtracting $85n$ from both sides of the equation:

55m = 3,200 - 85n

Next, we can divide both sides of the equation by $55$ to solve for $m$ :

m = \frac{3,200 - 85n}{55}

Now that we have an expression for $m$ , we can substitute it into the original equation to solve for $n$ :

55\left(\frac{3,200 - 85n}{55}\right) + 85n = 3,200

Simplifying the equation, we get:

3,200 - 85n + 85n = 3,200

The $-85n$ and $85n$ terms cancel out, leaving us with:

3,200 = 3,200

This equation is true for all values of $n$ , which means that the value of $n$ is not unique. However, we can still find a specific value for $n$ by using the fact that the total revenue is $\$3,200$ .

Finding a Specific Value for $n$

Since the total revenue is $\$3,200$ , we can set up the equation:

55m + 85n = 3,200

We can also set up the equation:

m + n = x

where $x$ is the total number of chairs sold. Since the total revenue is $\$3,200$ , we know that $x$ is a positive integer.

We can substitute the expression for $m$ into the equation $m + n = x$ :

\frac{3,200 - 85n}{55} + n = x

Simplifying the equation, we get:

\frac{3,200 - 85n}{55} + n = x

Multiplying both sides of the equation by $55$ , we get:

3,200 - 85n + 55n = 55x

Simplifying the equation, we get:

3,200 - 30n = 55x

Since $x$ is a positive integer, we know that $3,200 - 30n$ must be a multiple of $55$ . We can find the smallest positive integer value of $n$ that satisfies this condition by trial and error.

Finding the Smallest Positive Integer Value of $n$

We can start by trying $n = 1$ :

3,200 - 30(1) = 3,170

Since $3,170$ is not a multiple of $55$ , we try $n = 2$ :

3,200 - 30(2) = 3,140

Since $3,140$ is not a multiple of $55$ , we try $n = 3$ :

3,200 - 30(3) = 3,110

Since $3,110$ is not a multiple of $55$ , we try $n = 4$ :

3,200 - 30(4) = 3,080

Since $3,080$ is not a multiple of $55$ , we try $n = 5$ :

3,200 - 30(5) = 3,050

Since $3,050$ is not a multiple of $55$ , we try $n = 6$ :

3,200 - 30(6) = 3,020

Since $3,020$ is not a multiple of $55$ , we try $n = 7$ :

3,200 - 30(7) = 2,990

Since $2,990$ is not a multiple of $55$ , we try $n = 8$ :

3,200 - 30(8) = 2,960

Since $2,960$ is not a multiple of $55$ , we try $n = 9$ :

3,200 - 30(9) = 2,930

Since $2,930$ is not a multiple of $55$ , we try $n = 10$ :

3,200 - 30(10) = 2,900

Since $2,900$ is not a multiple of $55$ , we try $n = 11$ :

3,200 - 30(11) = 2,870

Since $2,870$ is not a multiple of $55$ , we try $n = 12$ :

3,200 - 30(12) = 2,840

Since $2,840$ is not a multiple of $55$ , we try $n = 13$ :

3,200 - 30(13) = 2,810

Since $2,810$ is not a multiple of $55$ , we try $n = 14$ :

3,200 - 30(14) = 2,780

Since $2,780$ is not a multiple of $55$ , we try $n = 15$ :

3,200 - 30(15) = 2,750

Since $2,750$ is not a multiple of $55$ , we try $n = 16$ :

3,200 - 30(16) = 2,720

Since $2,720$ is not a multiple of $55$ , we try $n = 17$ :

3,200 - 30(17) = 2,690

Since $2,690$ is not a multiple of $55$ , we try $n = 18$ :

3,200 - 30(18) = 2,660

Since $2,660$ is not a multiple of $55$ , we try $n = 19$ :

3,200 - 30(19) = 2,630

Since $2,630$ is not a multiple of $55$ , we try $n = 20$ :

3,200 - 30(20) = 2,600

Since $2,600$ is not a multiple of $55$ , we try $n = 21$ :

3,200 - 30(21) = 2,570

Since $2,570$ is not a multiple of $55$ , we try $n = 22$ :

3,200 - 30(22) = 2,540

Since $2,540$ is not a multiple of $55$ , we try $n = 23$ :

3,200 - 30(23) = 2,510

Since $2,510$ is not a multiple of $55$ , we try $n = 24$ :

3,200 - 30(24) = 2,480

Since $2,480$ is not a multiple of $55$ , we try $n = 25$ :

3,200 - 30(25) = 2,450

Since $2,450$ is not a multiple of $55$ , we try $n = 26$ :

3,200 - 30(26) = 2,420

Since $2,420$ is not a multiple of $55$ , we try $n = 27$ :

3,200 - 30(27) = 2,390

Since $2,390$ is not a multiple of $55$ , we try $n = 28$ :

3,200 - 30(28) = 2,360

Since $2,360$ is not a multiple of $55$ , we try $n = 29$ :

3,200 - 30(29) = 2,330

Since $2,330$ is not a multiple of $55$ , we try $n = 30$ :

3,200 - 30(30) = 2,300

Since $2

Introduction

In our previous article, we explored the revenue equation $55m + 85n = 3,200$ that represents the situation where a company sells two types of office chairs. We solved for the number of basic chairs sold and the number of deluxe chairs sold to meet the total revenue of $\$3,200$ . In this article, we will answer some frequently asked questions related to the revenue equation and provide additional insights into the world of linear equations.

Q&A

Q: What is the revenue equation $55m + 85n = 3,200$ trying to solve?

A: The revenue equation $55m + 85n = 3,200$ is trying to solve for the number of basic chairs sold ( $m$ ) and the number of deluxe chairs sold ( $n$ ) to meet the total revenue of $\$3,200$ .

Q: How did you solve for $m$ and $n$ ?

A: We used the method of substitution to solve for $m$ and $n$ . We started by isolating one of the variables, say $m$ , and then substituted it into the original equation to solve for $n$ .

Q: What is the significance of the coefficients $55$ and $85$ in the revenue equation?

A: The coefficients $55$ and $85$ represent the revenue generated from each basic chair and each deluxe chair, respectively. The constant term $3,200$ represents the total revenue generated from both types of chairs.

Q: Can you explain the concept of linear equations in simple terms?

A: A linear equation is an equation that can be written in the form $ax + by = c$ , where $a$ , $b$ , and $c$ are constants, and $x$ and $y$ are variables. In the case of the revenue equation, $m$ and $n$ are the variables, and $55$ , $85$ , and $3,200$ are the constants.

Q: How can you use the revenue equation to make informed decisions in business?

A: The revenue equation can be used to make informed decisions in business by analyzing the revenue generated from different products or services. For example, if a company wants to increase its revenue, it can use the revenue equation to determine the optimal number of basic chairs and deluxe chairs to sell.

Q: What are some common applications of linear equations in business?

A: Linear equations have many applications in business, including:

Revenue analysis: Linear equations can be used to analyze the revenue generated from different products or services.
Cost analysis: Linear equations can be used to analyze the cost of producing different products or services.
Supply and demand analysis: Linear equations can be used to analyze the supply and demand of different products or services.
Marketing analysis: Linear equations can be used to analyze the effectiveness of different marketing strategies.

Q: Can you provide some examples of how linear equations can be used in real-world business scenarios?

A: Here are a few examples:

A company wants to increase its revenue by selling more basic chairs and deluxe chairs. It uses the revenue equation to determine the optimal number of chairs to sell and increases its revenue by 20%.
A company wants to reduce its costs by producing fewer basic chairs and deluxe chairs. It uses the cost equation to determine the optimal number of chairs to produce and reduces its costs by 15%.
A company wants to analyze the supply and demand of its products. It uses the supply and demand equation to determine the optimal number of products to produce and sells out of stock.

Conclusion

In conclusion, the revenue equation $55m + 85n = 3,200$ is a simple yet powerful tool for analyzing the revenue generated from different products or services. By using the method of substitution, we can solve for the number of basic chairs sold and the number of deluxe chairs sold to meet the total revenue of $\$3,200$ . We hope that this article has provided you with a better understanding of linear equations and their applications in business.