A Car Dealership Sells 200 Vehicles In The Month Of June And Then Sells $\frac{1}{4}$ More Vehicles In The Month Of July. This Can Be Modeled By The Numerical Expression $200+\frac{1}{4}(200$\]. Simplify The Expression To Find How Many

Introduction

In the world of business, understanding sales trends and patterns is crucial for making informed decisions. A car dealership's sales can be a great example of this. In this article, we will explore how to model and simplify a numerical expression representing the car dealership's sales in two consecutive months.

The Problem

A car dealership sells 200 vehicles in the month of June. Then, in the month of July, they sell $\frac{1}{4}$ more vehicles than in June. We need to find out how many vehicles the dealership sold in total in July.

Modeling the Sales

To model the sales, we can use a numerical expression. Let's denote the number of vehicles sold in June as $200$. Then, the number of vehicles sold in July can be represented as $200 + \frac{1}{4}(200)$.

Simplifying the Expression

To simplify the expression, we need to follow the order of operations (PEMDAS):

1. Multiply $200$ by $\frac{1}{4}$: $200 \times \frac{1}{4} = 50$
2. Add $50$ to $200$: $200 + 50 = 250$

The Final Answer

Therefore, the car dealership sold a total of $250$ vehicles in July.

Conclusion

In this article, we modeled and simplified a numerical expression representing a car dealership's sales in two consecutive months. By following the order of operations, we were able to find the total number of vehicles sold in July. This example demonstrates the importance of understanding numerical expressions and how they can be used to model real-world scenarios.

Additional Examples

Here are a few more examples of numerical expressions that can be simplified:

• $300 + \frac{1}{2}(300)$
• $400 - \frac{1}{3}(400)$
• $500 + \frac{3}{4}(500)$

Tips and Tricks

When simplifying numerical expressions, remember to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following these tips and tricks, you can simplify numerical expressions with ease and become a master of mathematical modeling.

Real-World Applications

Numerical expressions are used in a wide range of real-world applications, including:

• Business: Modeling sales trends and patterns
• Science: Calculating quantities and rates
• Engineering: Designing and optimizing systems
• Finance: Calculating interest rates and investments

Final Thoughts

In conclusion, numerical expressions are a powerful tool for modeling and simplifying real-world scenarios. By following the order of operations and using the correct mathematical operations, we can simplify even the most complex expressions. Whether you're a business owner, scientist, engineer, or finance professional, understanding numerical expressions is essential for making informed decisions and achieving success.

Introduction

In our previous article, we explored how to model and simplify a numerical expression representing a car dealership's sales in two consecutive months. In this article, we will answer some frequently asked questions (FAQs) related to the topic.

Q&A

Q: What is the numerical expression for the car dealership's sales in July?

A: The numerical expression for the car dealership's sales in July is $200 + \frac{1}{4}(200)$.

Q: How do I simplify the numerical expression?

A: To simplify the numerical expression, you need to follow the order of operations (PEMDAS):

1. Multiply $200$ by $\frac{1}{4}$: $200 \times \frac{1}{4} = 50$
2. Add $50$ to $200$: $200 + 50 = 250$

Q: What is the total number of vehicles sold in July?

A: The total number of vehicles sold in July is $250$.

Q: Can I use this method to model sales for other months?

A: Yes, you can use this method to model sales for other months. Simply replace the number of vehicles sold in June with the actual number of vehicles sold in that month.

Q: How do I calculate the number of vehicles sold in a month if I don't know the exact number?

A: If you don't know the exact number of vehicles sold in a month, you can use an estimate or a range of values. For example, if you think the dealership sold between $200$ and $300$ vehicles in June, you can use $200 + \frac{1}{4}(200)$ or $200 + \frac{1}{4}(300)$ to model the sales.

Q: Can I use this method to model sales for other types of businesses?

A: Yes, you can use this method to model sales for other types of businesses. Simply replace the number of vehicles sold with the actual number of products or services sold.

Q: What are some common mistakes to avoid when simplifying numerical expressions?

A: Some common mistakes to avoid when simplifying numerical expressions include:

• Not following the order of operations (PEMDAS)
• Not evaluating expressions inside parentheses first
• Not multiplying and dividing from left to right
• Not adding and subtracting from left to right

Q: How can I practice simplifying numerical expressions?

A: You can practice simplifying numerical expressions by working through examples and exercises. You can also use online resources or math software to help you practice.

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to modeling and simplifying numerical expressions. By following the order of operations and using the correct mathematical operations, you can simplify even the most complex expressions. Whether you're a business owner, scientist, engineer, or finance professional, understanding numerical expressions is essential for making informed decisions and achieving success.

Additional Resources

• Mathematical Operations
• Numerical Expressions
• Simplifying Numerical Expressions

Final Thoughts

In conclusion, numerical expressions are a powerful tool for modeling and simplifying real-world scenarios. By following the order of operations and using the correct mathematical operations, you can simplify even the most complex expressions. Whether you're a business owner, scientist, engineer, or finance professional, understanding numerical expressions is essential for making informed decisions and achieving success.