Representing the Problem with an Equation

Oct 13, 2025 by thesweetdesigns.com 64 views

Introduction

In this article, we will delve into the world of mathematics and solve a problem that involves algebraic equations. Thomas, a keen walker, has been tracking his daily mileage for a week. On the first day of the week, he walked an impressive 6 miles. However, on the other days of the week, he walked a certain number of miles, denoted by the variable $$z$$. Our goal is to determine how many miles Thomas walked on the other days of the week.

Understanding the Problem

Let's break down the problem and understand what information we have. We know that Thomas walked a total of 30 miles in one week. This includes the 6 miles he walked on the first day. Therefore, the remaining miles he walked on the other days of the week can be represented by the variable $$z$$. We need to find the value of $$z$$.

Representing the Problem with an Equation

To represent this problem mathematically, we can use an equation. Let's denote the total number of miles Thomas walked in a week as $$T$$. We know that $$T = 30$$. We also know that Thomas walked 6 miles on the first day, and $$z$$ miles on the other days of the week. Since there are 6 days in a week, the number of miles Thomas walked on the other days can be represented as $$6z$$. Therefore, the equation representing this problem is:

T = 6 + 6z

Solving the Equation

Now that we have the equation, let's solve for $$z$$. We can start by subtracting 6 from both sides of the equation:

T - 6 = 6z

Since we know that $$T = 30$$, we can substitute this value into the equation:

30 - 6 = 6z

Simplifying the equation, we get:

24 = 6z

To solve for $$z$$, we can divide both sides of the equation by 6:

z = \frac{24}{6}

Simplifying the fraction, we get:

z = 4

Conclusion

In this article, we solved a problem that involved algebraic equations. We represented the problem mathematically using an equation and solved for the variable $$z$$. We found that Thomas walked 4 miles on the other days of the week. This problem demonstrates the importance of algebraic equations in solving real-world problems.

Real-World Applications

This problem has real-world applications in various fields, such as:

Fitness and Exercise: Understanding how to calculate total mileage walked in a week can help individuals set realistic fitness goals and track their progress.
Transportation: Calculating total mileage walked in a week can help individuals plan their daily routes and estimate the time it takes to complete a journey.
Business: Understanding how to calculate total mileage walked in a week can help businesses plan their logistics and estimate the cost of transportation.

Future Directions

In the future, we can explore more complex problems that involve algebraic equations. Some possible directions include:

Systems of Equations: We can explore how to solve systems of equations that involve multiple variables and equations.
Inequalities: We can explore how to solve inequalities that involve multiple variables and constraints.
Graphing: We can explore how to graph functions and equations to visualize the relationships between variables.

Conclusion

In conclusion, this article demonstrated how to solve a problem that involved algebraic equations. We represented the problem mathematically using an equation and solved for the variable $$z$$. We found that Thomas walked 4 miles on the other days of the week. This problem has real-world applications in various fields, and we can explore more complex problems in the future.

Introduction

In our previous article, we solved a problem that involved algebraic equations. We represented the problem mathematically using an equation and solved for the variable $$z$$. We found that Thomas walked 4 miles on the other days of the week. In this article, we will answer some frequently asked questions related to this problem.

Q&A Session

Q1: What is the total number of miles Thomas walked in a week?

A1: The total number of miles Thomas walked in a week is 30 miles.

Q2: How many miles did Thomas walk on the first day of the week?

A2: Thomas walked 6 miles on the first day of the week.

Q3: How many miles did Thomas walk on the other days of the week?

A3: Thomas walked 4 miles on the other days of the week.

Q4: What is the equation that represents this problem?

A4: The equation that represents this problem is:

T = 6 + 6z

Q5: How do we solve for the variable $$z$$?

A5: To solve for the variable $$z$$, we can start by subtracting 6 from both sides of the equation:

T - 6 = 6z

Then, we can substitute the value of $$T$$ into the equation and simplify:

24 = 6z

Finally, we can divide both sides of the equation by 6 to solve for $$z$$:

z = \frac{24}{6}

Q6: What is the value of $$z$$?

A6: The value of $$z$$ is 4.

Q7: What are some real-world applications of this problem?

A7: Some real-world applications of this problem include:

Fitness and Exercise: Understanding how to calculate total mileage walked in a week can help individuals set realistic fitness goals and track their progress.
Transportation: Calculating total mileage walked in a week can help individuals plan their daily routes and estimate the time it takes to complete a journey.
Business: Understanding how to calculate total mileage walked in a week can help businesses plan their logistics and estimate the cost of transportation.

Q8: Can we explore more complex problems that involve algebraic equations?

A8: Yes, we can explore more complex problems that involve algebraic equations. Some possible directions include:

Systems of Equations: We can explore how to solve systems of equations that involve multiple variables and equations.
Inequalities: We can explore how to solve inequalities that involve multiple variables and constraints.
Graphing: We can explore how to graph functions and equations to visualize the relationships between variables.

Conclusion

In this article, we answered some frequently asked questions related to the problem of Thomas walking 30 miles in one week. We represented the problem mathematically using an equation and solved for the variable $$z$$. We found that Thomas walked 4 miles on the other days of the week. This problem has real-world applications in various fields, and we can explore more complex problems in the future.

Frequently Asked Questions

What is the total number of miles Thomas walked in a week?
How many miles did Thomas walk on the first day of the week?
How many miles did Thomas walk on the other days of the week?
What is the equation that represents this problem?
How do we solve for the variable $$z$$?
What is the value of $$z$$?
What are some real-world applications of this problem?
Can we explore more complex problems that involve algebraic equations?

Glossary

Algebraic Equation: An equation that involves variables and constants.
Variable: A symbol that represents a value that can change.
Constant: A value that does not change.
System of Equations: A set of equations that involve multiple variables and equations.
Inequality: An equation that involves a variable and a constant, but with a greater-than or less-than symbol.
Graphing: The process of visualizing the relationships between variables using a graph.

References

Thomas Walked 30 Miles in One Week: A Mathematical Approach (previous article)
Algebraic Equations (online resource)
Systems of Equations (online resource)
Inequalities (online resource)
Graphing (online resource)