Andrew Pays A Monthly Membership Fee Of $ 10 \$10 $10 At His Gym. Each Time He Uses The Gym, He Pays $ 5 \$5 $5 . Last Month, Andrew Spent A Total Of $ 65 \$65 $65 For Membership And Gym Use.If The Equation 10 + 5 X = 65 10 + 5x = 65 10 + 5 X = 65 Models The

Introduction

In this article, we will delve into the world of mathematics and explore a real-life scenario involving Andrew's gym membership. Andrew pays a monthly membership fee of $\$10$ at his gym, and each time he uses the gym, he pays an additional $\$5$. Last month, Andrew spent a total of $\$65$ for membership and gym use. We will use the equation $10 + 5x = 65$ to model this situation and solve for the number of times Andrew used the gym.

Understanding the Equation

The equation $10 + 5x = 65$ represents the total amount Andrew spent on his gym membership and gym use. The variable $x$ represents the number of times Andrew used the gym. The equation can be broken down into two parts: the fixed cost of the membership fee ($10) and the variable cost of using the gym ($5x$).

Solving the Equation

To solve the equation, we need to isolate the variable $x$. We can start by subtracting $10$ from both sides of the equation:

$$10 + 5x - 10 = 65 - 10$$

This simplifies to:

$$5x = 55$$

Next, we can divide both sides of the equation by $5$ to solve for $x$:

$$\frac{5x}{5} = \frac{55}{5}$$

This gives us:

$$x = 11$$

Interpretation of the Results

The solution to the equation, $x = 11$, tells us that Andrew used the gym $11$ times last month. This means that the total amount Andrew spent on his gym membership and gym use ($\$65$) can be broken down into the fixed cost of the membership fee ($\$10$) and the variable cost of using the gym ($\$55$).

Conclusion

In this article, we used the equation $10 + 5x = 65$ to model Andrew's gym membership dilemma. By solving the equation, we were able to determine that Andrew used the gym $11$ times last month. This scenario illustrates the importance of understanding and solving equations in real-life situations.

Real-World Applications

The concept of solving equations is essential in various fields, including mathematics, science, and engineering. In the context of Andrew's gym membership, the equation $10 + 5x = 65$ can be used to model other real-life scenarios, such as:

• Calculating the total cost of a product or service based on a fixed cost and a variable cost.
• Determining the number of units sold based on a fixed cost and a variable cost.
• Modeling the growth of a population based on a fixed rate and a variable rate.

Tips and Tricks

When solving equations, it's essential 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 steps and using the correct order of operations, you can solve equations with confidence and accuracy.

Common Mistakes to Avoid

When solving equations, it's essential to avoid common mistakes, such as:

• Forgetting to isolate the variable.
• Not following the order of operations.
• Making errors when subtracting or adding numbers.

By being aware of these common mistakes, you can avoid them and ensure that your solutions are accurate and reliable.

Conclusion

$$$$

Introduction

In our previous article, we explored the world of mathematics and used the equation $10 + 5x = 65$ to model Andrew's gym membership dilemma. We solved for the number of times Andrew used the gym and found that he used the gym $11$ times last month. In this article, we will answer some frequently asked questions related to the equation and provide additional insights.

Q&A

Q: What is the equation $10 + 5x = 65$ modeling?

A: The equation $10 + 5x = 65$ models Andrew's gym membership dilemma, where he pays a monthly membership fee of $\$10$ and each time he uses the gym, he pays an additional $\$5$. The equation represents the total amount Andrew spent on his gym membership and gym use.

Q: How did you solve the equation $10 + 5x = 65$?

A: To solve the equation, we first subtracted $10$ from both sides of the equation to isolate the variable $x$. This gave us $5x = 55$. Then, we divided both sides of the equation by $5$ to solve for $x$, which gave us $x = 11$.

Q: What does the solution $x = 11$ mean?

A: The solution $x = 11$ means that Andrew used the gym $11$ times last month. This is the number of times he paid the additional $\$5$ fee for using the gym.

Q: Can you explain the concept of a variable in the equation?

A: In the equation $10 + 5x = 65$, the variable $x$ represents the number of times Andrew used the gym. The variable is a placeholder for a value that we don't know yet, and we use it to represent the unknown quantity.

Q: How can you use the equation $10 + 5x = 65$ in real-life situations?

A: The equation $10 + 5x = 65$ can be used to model various real-life scenarios, such as calculating the total cost of a product or service based on a fixed cost and a variable cost, determining the number of units sold based on a fixed cost and a variable cost, or modeling the growth of a population based on a fixed rate and a variable rate.

Q: What are some common mistakes to avoid when solving equations?

A: Some common mistakes to avoid when solving equations include forgetting to isolate the variable, not following the order of operations, and making errors when subtracting or adding numbers.

Q: How can you ensure that your solutions are accurate and reliable?

A: To ensure that your solutions are accurate and reliable, follow the order of operations (PEMDAS), be careful when subtracting or adding numbers, and double-check your work.

Conclusion

In this article, we answered some frequently asked questions related to the equation $10 + 5x = 65$ and provided additional insights. We hope that this Q&A article has helped to clarify any doubts and provided a better understanding of the equation and its applications.

Real-World Applications

The concept of solving equations is essential in various fields, including mathematics, science, and engineering. In the context of Andrew's gym membership, the equation $10 + 5x = 65$ can be used to model other real-life scenarios, such as:

• Calculating the total cost of a product or service based on a fixed cost and a variable cost.
• Determining the number of units sold based on a fixed cost and a variable cost.
• Modeling the growth of a population based on a fixed rate and a variable rate.

Tips and Tricks

When solving equations, it's essential 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 steps and using the correct order of operations, you can solve equations with confidence and accuracy.

Common Mistakes to Avoid

When solving equations, it's essential to avoid common mistakes, such as:

• Forgetting to isolate the variable.
• Not following the order of operations.
• Making errors when subtracting or adding numbers.

By being aware of these common mistakes, you can avoid them and ensure that your solutions are accurate and reliable.

Conclusion

In conclusion, solving the equation $10 + 5x = 65$ allowed us to determine that Andrew used the gym $11$ times last month. This scenario illustrates the importance of understanding and solving equations in real-life situations. By following the order of operations and avoiding common mistakes, you can solve equations with confidence and accuracy.